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curve #3658

y2 = x3 − 11417299959756x + 14781466634060057456
a-invariants
[0, 0, 0, -11417299959756, 14781466634060057456]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/4ℤ
conductor (N)
194542926481728
discriminant (Δ)
862707017239744704227099870361478889472
Faltings height
6.3162
naive height
101.8121
primes of bad reduction
2, 3, 11, 29, 67, 97, 101, 1613
regulator
3236770.8944167730102420023077731152088904277085866
submitted by
Michael Rubinstein
submitted at
last updated

Witness: 6 independent points log in to add more points →

Commentary

Specialization at t = 13/16 of the Elkies-Klagsbrun Z/4 fibration E1: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = (8t-1)(32t+7), c = 8(t+1)(15t-8)(31t-7) (arXiv:2003.00077, eq. (5)), 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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