Magma V2.18-8     Wed Sep  5 2012 13:11:14 on luna     [Seed = 369194258]
Type ? for help.  Type <Ctrl>-D to quit.

Loading file "rationalpoints5tuples.mg"
Version 24/7/2012
> Cuenta00({0,1,2,4,7},{1,4,7},2,1);                                                                                                                                     

=================================================
=========      { 0, 1, 2, 4, 7 }      =========
=================================================

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
==== J= { 1, 4, 7 } ; {j1,j2}={2,1} ==== 
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

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

::: (1,1)   :::   (1)*(t^2 - 10/3*t + 2)*(t^2 + 1/3*(-2*a - 10)*t + 1/3*(4*a + 14))

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

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

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

$$$$$$$$$$ [OK]  --------> [ (1 : 0), (1 : 0) ]

t=oo -> (q,a)=(0,1) --> [ 1, 1, 1, 1, 1 ]

::: (1,1)   :::   (2)*(t^2 - 10/3*t + 2)*(t^2 + 1/3*(-2*a - 10)*t + 1/3*(4*a + 14))

        *** Elliptic curve base point = (1/2*(a + 2) : 1/2*(-a + 4) : 1)

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

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

#####   Rank = 2 > 1

::: (2,1)   :::   (2)*(t^2 - 6*t + 2)*(t^2 + 1/3*(-2*a - 10)*t + 1/3*(4*a + 14))

$$$$$$$$$$ [OK] Bruin-Stoll ------------> #Hk=0

::: (1,1)   :::   (3)*(t^2 - 10/3*t + 2)*(t^2 + 1/3*(-2*a - 10)*t + 1/3*(4*a + 14))

        *** Elliptic curve base point = (1/13*(-6*a - 9) : 1/169*(861*a + 2739) : 1)

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

          - RankBound for delta = 3 --> r = 2

#####   Rank = 2 > 1

::: (2,1)   :::   (3)*(t^2 - 6*t + 2)*(t^2 + 1/3*(-2*a - 10)*t + 1/3*(4*a + 14))

$$$$$$$$$$ [OK] Bruin-Stoll ------------> #Hk=0

::: (1,1)   :::   (6)*(t^2 - 10/3*t + 2)*(t^2 + 1/3*(-2*a - 10)*t + 1/3*(4*a + 14))

        *** Elliptic curve base point = (0 : -2*a - 4 : 1)

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

          - RankBound for delta = 6 --> r = 1

$$$$$$$$$$ [OK]  --------> [ (0 : 1), (0 : 1) ]

t=0 -> (q,a)=(0,1) --> [ 1, 1, 1, 1, 1 ]

##############
 SOLUTION:
 {
[ 1, 1, 1, 1, 1 ]
}
##############
true {
    [ 1, 1, 1, 1, 1 ]
}
{ (1 : 0), (0 : 1) }
<{ 0, 1, 2, 4, 7 }, { 1, 4, 7 }, [ 2, 1 ], 10, [ 1, 2, 3, 6 ], <1, <[ 1, 1 ], t^2 - 10/3*t + 2, t^2 + 1/3*(-2*a - 10)*t + 1/3*(4*a + 14)>, <<1, -1, 0>, <-2*a - 20, -24*a 
    - 100, 28*a + 40, 336*a + 916, 0>, <(0 : 0 : 1), (-10 : -24*a - 120 : 1)>, 1, <(1 : 0)>, <[ 1, 1, 1, 1, 1 ]>>>, <2, <[ 2, 1 ], t^2 - 6*t + 2, t^2 + 1/3*(-2*a - 10)*t 
    + 1/3*(4*a + 14)>, <"Bruin-Stoll">>, <3, <[ 2, 1 ], t^2 - 6*t + 2, t^2 + 1/3*(-2*a - 10)*t + 1/3*(4*a + 14)>, <"Bruin-Stoll">>, <6, <[ 1, 1 ], t^2 - 10/3*t + 2, t^2 +
    1/3*(-2*a - 10)*t + 1/3*(4*a + 14)>, <<0, -2*a - 4, 1>, <2*a - 20, 24*a - 100, -28*a + 40, -336*a + 916, 0>, <(0 : 28*a - 40 : 1), (-10 : 24*a - 120 : 1)>, 1, <(0 : 
1)>, <[ 1, 1, 1, 1, 1 ]>>>>
>