curve #1937

y² + xy + y = x³ − 314261798247699281583485627025593248x + 67755045622702867235372184283705632291457304269577006

a-invariants: [1, 0, 1, -314261798247699281583485627025593248, 67755045622702867235372184283705632291457304269577006]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/3ℤ
conductor (N): 111542781755961338087181160322717314938023670 ☆ record for ℤ/3ℤ torsion, rank ≥ 13
discriminant (Δ): 3142941544018513004796438792218733474938920014925879832034929711618822032992476544195468428610070875000000
Faltings height: 19.1666
naive height: 256.8202
primes of bad reduction: 2, 3, 5, 13, 17, 19, 41, 53, 109, 193, 223, 239, 499, 641, 31729, 136177, 262971886729
regulator: 372801125543.2112829407605686036493595908682400129159043548111944
submitted by: dujella
submitted at: 2026-09-25 19:43:45 UTC
last updated: 2026-09-25 19:43:45 UTC

(331064222522331745, 108002572991933200465427)
(60302653368352270, 221412534637578854030048702)
(340457177749093345, 15004107520711561275138827)
(278817716186182945, 42525146455634850545742227)
(336710803989195745, 10677513423307188160561427)
(296643657499084225, 25202472452361902409344747)
(177447905093399842, 132579729686645884210002263)
(331615767977756020, 2887605493923435665798402)
(-47959331959652030, -287604798938943632624433673)
(240433217677549720, 78070900353018751873632077)
(331548647063699980, 2700485784265218800691617)
(340960186243818900, 15563361748866798001200322)
(343605917424468145, 18457352478941937160416827)

found by Elkies (2018)

last edited by dujella at 2026-09-25 19:43:45 UTC · history