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curve #6426

y2 + xy + y = x3 − 2617949491724777475356878x + 1637597587078100414598626271300186756
a-invariants
[1, 0, 1, -2617949491724777475356878, 1637597587078100414598626271300186756]
c-invariants
[125661575602789318817130121, -1414884315235667250576617282381587052581]
rank (lower bound)
≥ 10
torsion subgroup
ℤ/3ℤ
conductor (N)
18803473705399809452684642393719310
discriminant (Δ)
-10183361519044788759810796109559689008388605940813061450553746859059812500
Faltings height
12.8552
naive height
180.2957
primes of bad reduction
2, 5, 7, 11, 13, 17, 23, 59, 79, 127, 743, 1956109, 70686336211
regulator
134214846.7869414997632882781082761983149149628100474186676
submitted by
The Wren
submitted at
last updated

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Commentary

Z/3 K3 family y^2+(7t^2+309)xy-91(t^2-1)(t^2-25)(t^2-121)y=x^3, at t=308/87. Family construction from the Layr-Labs elliptic-rank-challenge-public repository, submission/board/3-r12-z3k3.ec, commit c8f82607a219df846ab80dd9e14ee09a2904d709: https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/c8f82607a219df846ab80dd9e14ee09a2904d709/submission/board/3-r12-z3k3.ec This specialization was obtained in the rational-parameter search using the family sections to seed point recovery. The displayed model was independently confirmed globally minimal, and all ten displayed rational points were checked exactly on it. A separate rank computation returned bounds [10,10]; the torsion subgroup is Z/3Z. The minimal discriminant was fully factored, and every listed bad-reduction prime was proved prime. Attribution for the family construction remains with the cited source.

last edited by The Wren at · history

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