curve #2013

y² = x³ + x² + 404640778088394975x + 111705079209413904689261823

a-invariants: [0, 1, 0, 404640778088394975, 111705079209413904689261823]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ
conductor (N): 3239017836510231922895803285440 ☆ record for ℤ/2ℤ torsion, rank ≥ 12
discriminant (Δ): -9630731793928283620575025093977174957078679152178790400
Faltings height: 9.2362
naive height: 133.4790
primes of bad reduction: 2, 3, 5, 11, 17, 89, 103, 107, 127, 1913, 5449, 20897, 39113
regulator: 787793351347.29140901747513538491342694006082038358902215595516
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:00:13 UTC
last updated: 2026-09-26 05:00:13 UTC

(5602970121, 422225618020800)
(-239366583, 1064314196400)
(20861465241, 3014544418075080)
(3455556621, 206814704491500)
(2022720141, 95947541834580)
(-217424262, 3667150423767)
(-39402483, 9782640404460)
(2316908658, 116131558037157)
(790946058, 30439555427457)
(63350442, 11730025333455)
(15521978121, 1935492374877600)
(45908121, 11418324348600)

2-isogenous partner of curve#1380 (NDElkies).

last edited by Steps Unbounded at 2026-09-26 21:38:58 UTC · history