Magma V2.18-8     Wed Sep  5 2012 13:11:24 on luna     [Seed = 1059609653]
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Loading file "rationalpoints5tuples.mg"
Version 24/7/2012
> Cuenta00({0,1,4,7,8},{1,4,7},2,1);                                                                                                                                     

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

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

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

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

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

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

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

#####   Rank = 1 > 1

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

        *** Elliptic curve base point = (1 : -9 : 0)

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

          - RankBound for delta = 1 --> r = 0

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

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

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

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

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

        *** Elliptic curve base point = (0 : -6 : 1)

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

          - RankBound for delta = -3 --> r = 0

$$$$$$$$$$ [OK]  --------> { (2 : 1), (0 : 1) }

t=2 -> (q,a)=(0,1) --> [ 1, 1, 1, 1, 1 ]
t=0 -> (q,a)=(0,1) --> [ 1, 1, 1, 1, 1 ]

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

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

##############
 SOLUTION:
 {
[ 1, 1, 1, 1, 1 ]
}
##############
true {
    [ 1, 1, 1, 1, 1 ]
}
{ (1 : 1), (2 : 1), (1 : 0), (0 : 1) }
<{ 0, 1, 4, 7, 8 }, { 1, 4, 7 }, [ 2, 1 ], 1, [ 1, 2, -3, -6 ], <1, <[ 1, 2 ], t^2 - 10/3*t + 2, t^2 - 2/3*t - 2/3>, <<1, -9, 0>, <0, -1, 0, -12, 0>, "Rank 0", 0, <(1 : 
1), (1 : 0)>, <[ 1, 1, 1, 1, 1 ]>>>, <2, <[ 1, 1 ], t^2 - 10/3*t + 2, t^2 + 2*t - 6>, <"Bruin-Stoll">>, <-3, <[ 1, 1 ], t^2 - 10/3*t + 2, t^2 + 2*t - 6>, <<0, -6, 1>, <0,
-1, 0, -12, 0>, "Rank 0", 0, <(2 : 1), (0 : 1)>, <[ 1, 1, 1, 1, 1 ]>>>, <-6, <[ 1, 1 ], t^2 - 10/3*t + 2, t^2 + 2*t - 6>, <"Bruin-Stoll">>>
>