curve #4310

y² + xy = x³ − 78140864021061514x + 8218816559619570607120019

a-invariants

[1, 0, 0, -78140864021061514, 8218816559619570607120019]

c-invariants

[3750761473010952673, -7101057513137451214068125425]

rank (lower bound)

≥ 8

torsion subgroup

ℤ/2ℤ × ℤ/2ℤ

conductor (N)

975919424884519423407

discriminant (Δ)

1355027986931801654571132459855357820269268608208689

Faltings height

8.5935

naive height

128.3055

primes of bad reduction

3, 11, 19, 31, 37, 73, 79, 127, 397, 733, 6367

regulator

126713907.918079679679454246081602464607809616925607795

submitted by

Volkan Dagli

submitted at

2026-10-17 09:47:38 UTC

later contributions

(202230830, 828766452653)
(4400717470/9, -251727179634041/27)
(75174832895/196, -16157623183571717/2744)
(555148304510/1681, 295877677289361553/68921)
(4616803886/25, -36753454074131/125)
(4149446330, -266701811451733)
(100968021995/484, -10629143699133331/10648)
(5846018971934/21025, -8616997508945176063/3048625)

Rational 2-isogeny of 4-8.ec from Layr Labs / Yukon Elliptic Rank Challenge via pCwOrM Werr Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 09:47:38 UTC · history