Magma V2.18-8     Wed Sep  5 2012 13:11:19 on luna     [Seed = 51666946]
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Loading file "rationalpoints5tuples.mg"
Version 24/7/2012
> Cuenta00({0,1,3,7,8},{1,3,7},3,3);                                                                                                                                     

=================================================
=========      { 0, 1, 3, 7, 8 }      =========
=================================================

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
==== J= { 1, 3, 7 } ; {j1,j2}={3,3} ==== 
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

D=7 --> deltas=[ 1, -1, 2, -2 ]

::: (1,1)   :::   (1)*(t^2 + 1/2*(a - 7)*t + 1/2*(-a + 4))*(t^2 + 1/2*(a + 1)*t + 1/2*(-a - 4))

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

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

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

$$$$$$$$$$ [OK]  --------> [ (1 : 0), (4 : 1), (1 : 1), (4 : 1), (5/6 : 1), (1 : 1), (1 : 0), (5/6 : 1) ]

t=4 -> (q,a)=(120,1) --> [ 1, 121, 361, 841, 961 ]
t=5/6 -> (q,a)=(120,1) --> [ 1, 121, 361, 841, 961 ]
t=1 -> (q,a)=(0,1) --> [ 1, 1, 1, 1, 1 ]
t=oo -> (q,a)=(0,1) --> [ 1, 1, 1, 1, 1 ]

::: (1,1)   :::   (-1)*(t^2 + 1/2*(a - 7)*t + 1/2*(-a + 4))*(t^2 + 1/2*(a + 1)*t + 1/2*(-a - 4))

        *** Elliptic curve base point = (0 : -3/2 : 1)

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

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

$$$$$$$$$$ [OK]  --------> [ (0 : 1), (9/5 : 1), (0 : 1), (9/5 : 1), (3/8 : 1), (3/2 : 1), (3/2 : 1), (3/8 : 1) ]

t=3/2 -> (q,a)=(0,1) --> [ 1, 1, 1, 1, 1 ]
t=3/8 -> (q,a)=(120,1) --> [ 1, 121, 361, 841, 961 ]
t=0 -> (q,a)=(0,1) --> [ 1, 1, 1, 1, 1 ]
t=9/5 -> (q,a)=(120,1) --> [ 1, 121, 361, 841, 961 ]

::: (1,1)   :::   (2)*(t^2 + 1/2*(a - 7)*t + 1/2*(-a + 4))*(t^2 + 1/2*(a + 1)*t + 1/2*(-a - 4))

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

::: (1,1)   :::   (-2)*(t^2 + 1/2*(a - 7)*t + 1/2*(-a + 4))*(t^2 + 1/2*(a + 1)*t + 1/2*(-a - 4))

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

##############
 SOLUTION:
 {
[ 1, 121, 361, 841, 961 ],
[ 1, 1, 1, 1, 1 ]
}
##############
true {
    [ 1, 121, 361, 841, 961 ],
    [ 1, 1, 1, 1, 1 ]
}
{ (1 : 1), (3/8 : 1), (3/2 : 1), (4 : 1), (1 : 0), (9/5 : 1), (5/6 : 1), (0 : 1) }
<{ 0, 1, 3, 7, 8 }, { 1, 3, 7 }, [ 3, 3 ], 7, [ 1, -1, 2, -2 ], <1, <[ 1, 1 ], t^2 + 1/2*(a - 7)*t + 1/2*(-a + 4), t^2 + 1/2*(a + 1)*t + 1/2*(-a - 4)>, <<1, -1, 0>, <a, 
    -a - 1, 1, 102*a - 270, 470*a - 1244>, <(-5*a + 14 : -21*a + 54 : 1), (a - 2 : a - 4 : 1)>, 1, <(1 : 1), (4 : 1), (1 : 0), (5/6 : 1)>, <[ 1, 121, 361, 841, 961 ], [ 
1, 1, 1, 1, 1 ]>>>, <-1, <[ 1, 1 ], t^2 + 1/2*(a - 7)*t + 1/2*(-a + 4), t^2 + 1/2*(a + 1)*t + 1/2*(-a - 4)>, <<0, -3/2, 1>, <a, a - 1, 1, -103*a - 270, -470*a - 1244>, 
<(5*a + 14 : -21*a - 55 : 1), (-a - 2 : a + 3 : 1)>, 1, <(3/8 : 1), (3/2 : 1), (9/5 : 1), (0 : 1)>, <[ 1, 121, 361, 841, 961 ], [ 1, 1, 1, 1, 1 ]>>>, <2, <[ 1, 1 ], t^2 +
    1/2*(a - 7)*t + 1/2*(-a + 4), t^2 + 1/2*(a + 1)*t + 1/2*(-a - 4)>, <"Bruin-Stoll">>, <-2, <[ 1, 1 ], t^2 + 1/2*(a - 7)*t + 1/2*(-a + 4), t^2 + 1/2*(a + 1)*t + 1/2*(-a
    - 4)>, <"Bruin-Stoll">>>
>