Magma V2.18-8     Wed Sep  5 2012 13:11:21 on luna     [Seed = 152988166]
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Loading file "rationalpoints5tuples.mg"
Version 24/7/2012
> 
> Cuenta00({0,1,4,7,8},{1,4,8},2,2);                                                                                                                                     

=================================================
=========      { 0, 1, 4, 7, 8 }      =========
=================================================

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
==== J= { 1, 4, 8 } ; {j1,j2}={2,2} ==== 
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

D=2 --> deltas=[ 1, 3, 7, 21 ]

::: (1,1)   :::   (1)*(t^2 - 5*t + 7/4)*(t^2 + 1/2*(-3*a - 1)*t + 7/4)

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

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

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

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

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

::: (1,1)   :::   (3)*(t^2 - 5*t + 7/4)*(t^2 + 1/2*(-3*a - 1)*t + 7/4)

        *** Elliptic curve base point = (1/2*(-3*a + 5) : 0 : 1)

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

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

$$$$$$$$$$ [OK]  --------> []


::: (1,1)   :::   (7)*(t^2 - 5*t + 7/4)*(t^2 + 1/2*(-3*a - 1)*t + 7/4)

        *** Elliptic curve base point = (1/2*(-3*a + 5) : 0 : 1)

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

          - RankBound for delta = 7 --> r = 1

$$$$$$$$$$ [OK]  --------> []


::: (1,1)   :::   (21)*(t^2 - 5*t + 7/4)*(t^2 + 1/2*(-3*a - 1)*t + 7/4)

        *** Elliptic curve base point = (1/2*(-3*a + 5) : 0 : 1)

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

          - RankBound for delta = 21 --> r = 3

#####   Rank = 3 > 1

::: (2,1)   :::   (21)*(t^2 - 3*t + 7/4)*(t^2 + 1/2*(-3*a - 1)*t + 7/4)

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

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

          - RankBound for delta = 21 --> r = 1

$$$$$$$$$$ [OK]  --------> []


##############
 SOLUTION:
 {
[ 1, 1, 1, 1, 1 ]
}
##############
true {
    [ 1, 1, 1, 1, 1 ]
}
{ (1 : 0), (0 : 1) }
<{ 0, 1, 4, 7, 8 }, { 1, 4, 8 }, [ 2, 2 ], 2, [ 1, 3, 7, 21 ], <1, <[ 1, 1 ], t^2 - 5*t + 7/4, t^2 + 1/2*(-3*a - 1)*t + 7/4>, <<1, -1, 0>, <0, 0, 0, -18*a - 15, -3038*a +
    4086>, <(22*a + 21 : -162*a - 144 : 1), (10*a - 6 : 0 : 1)>, 1, <(1 : 0), (0 : 1)>, <[ 1, 1, 1, 1, 1 ]>>>, <3, <[ 1, 1 ], t^2 - 5*t + 7/4, t^2 + 1/2*(-3*a - 1)*t + 
    7/4>, <<1/2*(-3*a + 5), 0, 1>, <0, a, 0, -2*a - 1, -113*a + 150>, <(3*a - 1 : -2*a + 8 : 1), (3*a - 2 : 0 : 1)>, 1, <>, <>>>, <7, <[ 1, 1 ], t^2 - 5*t + 7/4, t^2 + 
    1/2*(-3*a - 1)*t + 7/4>, <<1/2*(-3*a + 5), 0, 1>, <0, 0, 0, -882*a - 735, -1042034*a + 1401498>, <(1/289*(2170*a + 30891) : 1/4913*(1399734*a - 7618716) : 1), (70*a -
    42 : 0 : 1)>, 1, <>, <>>>, <21, <[ 2, 1 ], t^2 - 3*t + 7/4, t^2 + 1/2*(-3*a - 1)*t + 7/4>, <<1/2*(-a + 3), 0, 1>, <0, 0, 0, 882*a - 735, -1042034*a - 1401498>, 
<(1/4*(2240*a + 2961) : 1/8*(-170128*a - 239071) : 1), (70*a + 42 : 0 : 1)>, 1, <>, <>>>>
>