Magma V2.18-8     Wed Sep  5 2012 13:11:30 on luna     [Seed = 725370911]
Type ? for help.  Type <Ctrl>-D to quit.

Loading file "rationalpoints5tuples.mg"
Version 24/7/2012
> Cuenta({0,3,5,6,10});                                                                                                                                                  

=================================================
=========      { 0, 3, 5, 6, 10 }      =========
=================================================

=================================================
=========  { 0, 3, 5, 6, 10 } - { 0, 5, 10 }  =========
=================================================

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
==== J= { 0, 5, 10 } ; {j1,j2}={2,3} ==== 
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

D=-6 --> deltas=[ 1, -1, -5, 5 ]

::: (1,1)   :::   (1)*(t^2 + 1/5*(-2*a - 14)*t + 2)*(t^2 + 1/5*(-4*a - 8)*t + 1/5*(4*a - 2))

        *** Elliptic curve base point = (1 : -1 : 0)

        ***** h_K = 2 --> Integral Model

          - RankBound for delta = 1 --> r = 2

#####   Rank = 2 > 1

::: (2,1)   :::   (1)*(t^2 + 1/5*(2*a - 14)*t + 2)*(t^2 + 1/5*(-4*a - 8)*t + 1/5*(4*a - 2))

        *** Elliptic curve base point = (1 : -1 : 0)

        ***** h_K = 2 --> Integral Model

          - RankBound for delta = 1 --> r = 2

#####   Rank = 2 > 1

@@@@@@@@@@   UNKNOWN   @@@@@@@@@@

=================================================
=========  { 0, 3, 5, 6, 10 } - { 3, 5, 6 }  =========
=================================================

@@@@@@@@@@   BIQUADRATIC CASE   @@@@@@@@@@

=================================================
=========  { 0, 3, 5, 6, 10 } - { 3, 5, 10 }  =========
=================================================

@@@@@@@@@@   BIQUADRATIC CASE   @@@@@@@@@@

=================================================
=========  { 0, 3, 5, 6, 10 } - { 0, 3, 10 }  =========
=================================================

@@@@@@@@@@   BIQUADRATIC CASE   @@@@@@@@@@

=================================================
=========  { 0, 3, 5, 6, 10 } - { 0, 3, 6 }  =========
=================================================

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
==== J= { 0, 3, 6 } ; {j1,j2}={2,3} ==== 
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

D=10 --> deltas=[ 1, -1, 2, -2, -3, 3, -6, 6 ]

::: (1,1)   :::   (1)*(t^2 + 1/3*(2*a - 2)*t + 2)*(t^2 + 1/3*(4*a + 8)*t + 1/3*(-4*a - 14))

        *** Elliptic curve base point = (1 : -1 : 0)

        ***** h_K = 2 --> Integral Model

          - RankBound for delta = 1 --> r = 2

#####   Rank = 2 > 1

::: (2,1)   :::   (1)*(t^2 + 1/3*(-2*a - 2)*t + 2)*(t^2 + 1/3*(4*a + 8)*t + 1/3*(-4*a - 14))

        *** Elliptic curve base point = (1 : -1 : 0)

        ***** h_K = 2 --> Integral Model

          - RankBound for delta = 1 --> r = 2

#####   Rank = 2 > 1

@@@@@@@@@@   UNKNOWN   @@@@@@@@@@

=================================================
=========  { 0, 3, 5, 6, 10 } - { 5, 6, 10 }  =========
=================================================

@@@@@@@@@@   BIQUADRATIC CASE   @@@@@@@@@@

=================================================
=========  { 0, 3, 5, 6, 10 } - { 3, 6, 10 }  =========
=================================================

@@@@@@@@@@   BIQUADRATIC CASE   @@@@@@@@@@

=================================================
=========  { 0, 3, 5, 6, 10 } - { 0, 6, 10 }  =========
=================================================

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
==== J= { 0, 6, 10 } ; {j1,j2}={2,3} ==== 
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

D=-1 --> deltas=[ 1, -2, 3, -5, -6, 10, -15, -30 ]

::: (1,1)   :::   (1)*(t^2 + 1/2*(-3*a - 7)*t + 5/2)*(t^2 + 1/2*(5*a - 5)*t - 5/2*a)

        *** Elliptic curve base point = (1 : -1 : 0)

        ***** h_K = 1 --> Minimal Model

          - RankBound for delta = 1 --> r = 3

#####   Rank = 3 > 1

::: (2,1)   :::   (1)*(t^2 + 1/2*(3*a - 7)*t + 5/2)*(t^2 + 1/2*(5*a - 5)*t - 5/2*a)

        *** Elliptic curve base point = (1 : -1 : 0)

        ***** h_K = 1 --> Minimal Model

          - RankBound for delta = 1 --> r = 2

#####   Rank = 2 > 1

@@@@@@@@@@   UNKNOWN   @@@@@@@@@@

=================================================
=========  { 0, 3, 5, 6, 10 } - { 0, 3, 5 }  =========
=================================================

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
==== J= { 0, 3, 5 } ; {j1,j2}={2,3} ==== 
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

D=2 --> deltas=[ 1, -3, -5, 15 ]

::: (1,1)   :::   (1)*(t^2 + (-3*a + 1)*t + 5/2)*(t^2 + (5*a + 5)*t + 1/2*(-10*a - 15))

        *** Elliptic curve base point = (1 : -1 : 0)

        ***** h_K = 1 --> Minimal Model

          - RankBound for delta = 1 --> r = 2

#####   Rank = 2 > 1

::: (2,1)   :::   (1)*(t^2 + (3*a + 1)*t + 5/2)*(t^2 + (5*a + 5)*t + 1/2*(-10*a - 15))

        *** Elliptic curve base point = (1 : -1 : 0)

        ***** h_K = 1 --> Minimal Model

          - RankBound for delta = 1 --> r = 3

#####   Rank = 3 > 1

@@@@@@@@@@   UNKNOWN   @@@@@@@@@@

=================================================
=========  { 0, 3, 5, 6, 10 } - { 0, 5, 6 }  =========
=================================================

@@@@@@@@@@   BIQUADRATIC CASE   @@@@@@@@@@

@@@@@@@@@@   UNKNOWN   @@@@@@@@@@
I = { 0, 3, 5, 6, 10 }
  J = { 0, 5, 10 } [j1,j2] = [ 2, 3 ] --> Failure by: { Rank }
  J = { 0, 3, 6 } [j1,j2] = [ 2, 3 ] --> Failure by: { Rank }
  J = { 0, 6, 10 } [j1,j2] = [ 2, 3 ] --> Failure by: { Rank }
  J = { 0, 3, 5 } [j1,j2] = [ 2, 3 ] --> Failure by: { Rank }
false {}
{ Rank }
<{ 0, 3, 5, 6, 10 }, <<{ 0, 5, 10 }, [ 2, 3 ], -6, [ 1, -1, -5, 5 ], <1, <<[ 1, 1 ], t^2 + 1/5*(-2*a - 14)*t + 2, t^2 + 1/5*(-4*a - 8)*t + 1/5*(4*a - 2)>, <false, -1, 
"Failure by", <1, -1, 0>, <-6*a - 22, -52*a - 74, -126*a - 162, -2076*a - 687, 0>, 2, "Rank">>, <<[ 2, 1 ], t^2 + 1/5*(2*a - 14)*t + 2, t^2 + 1/5*(-4*a - 8)*t + 1/5*(4*a 
    - 2)>, <false, -1, "Failure by", <1, -1, 0>, <-2*a - 22, -76*a - 170, 6*a + 414, 2460*a + 561, 0>, 2, "Rank">>>>>, <<{ 0, 3, 6 }, [ 2, 3 ], 10, [ 1, -1, 2, -2, -3, 3,
-6, 6 ], <1, <<[ 1, 1 ], t^2 + 1/3*(2*a - 2)*t + 2, t^2 + 1/3*(4*a + 8)*t + 1/3*(-4*a - 14)>, <false, -1, "Failure by", <1, -1, 0>, <18*a + 18, 396*a + 1062, 13770*a + 
    44550, 280260*a + 918945, 0>, 2, "Rank">>, <<[ 2, 1 ], t^2 + 1/3*(-2*a - 2)*t + 2, t^2 + 1/3*(4*a + 8)*t + 1/3*(-4*a - 14)>, <false, -1, "Failure by", <1, -1, 0>, 
<2*a + 6, 84*a + 278, 890*a + 2610, 12540*a + 39985, 0>, 2, "Rank">>>>>, <<{ 0, 6, 10 }, [ 2, 3 ], -1, [ 1, -2, 3, -5, -6, 10, -15, -30 ], <1, <<[ 1, 1 ], t^2 + 1/2*(-3*a
    - 7)*t + 5/2, t^2 + 1/2*(5*a - 5)*t - 5/2*a>, <false, -1, "Failure by", <1, -1, 0>, <2, 6*a + 2, 2*a + 2, 10*a + 34, -14*a + 34>, 3, "Rank">>, <<[ 2, 1 ], t^2 + 
    1/2*(3*a - 7)*t + 5/2, t^2 + 1/2*(5*a - 5)*t - 5/2*a>, <false, -1, "Failure by", <1, -1, 0>, <2, 3*a - 7, 2*a + 2, -14*a - 38, -36*a + 188>, 2, "Rank">>>>>, <<{ 0, 3,
5 }, [ 2, 3 ], 2, [ 1, -3, -5, 15 ], <1, <<[ 1, 1 ], t^2 + (-3*a + 1)*t + 5/2, t^2 + (5*a + 5)*t + 1/2*(-10*a - 15)>, <false, -1, "Failure by", <1, -1, 0>, <0, 0, 0, -45,
-100>, 2, "Rank">>, <<[ 2, 1 ], t^2 + (3*a + 1)*t + 5/2, t^2 + (5*a + 5)*t + 1/2*(-10*a - 15)>, <false, -1, "Failure by", <1, -1, 0>, <0, 0, 0, -45, 100>, 3, "Rank">>>>>>
>