Elliptic Curve Rank Leaderboard

curve #3691

y2 + y = x3 + x2 − 4510044910x + 117917739750214
a-invariants
[0, 1, 1, -4510044910, 117917739750214]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/5ℤ
conductor (N)
10994568585
discriminant (Δ)
-135795635709244219536049096875
Faltings height
4.3977
naive height
78.3252
primes of bad reduction
3, 5, 7, 11, 13, 732239
regulator
305.8910313754455621270446339143097730910264338
submitted by
Michael Rubinstein
submitted at
last updated

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Commentary

Specialization at t = -91/495 of the universal curve with a 5-torsion point, y^2 + (t+1)xy + ty = x^3 + tx^2 (as searched in arXiv:2003.00077, Sec. 12), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).

last edited by Michael Rubinstein at · history

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