curve #6220

y² + xy = x³ − 226636699956243013046888877875730x + 1684533974946872884413789022232053656556284136452

a-invariants: [1, 0, 0, -226636699956243013046888877875730, 1684533974946872884413789022232053656556284136452]
c-invariants: [10878561597899664626250666138035041, -1455437354354098188451356112057991298640628700947089]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/3ℤ
conductor (N): 36739960730115773550895377256832735140590
discriminant (Δ): -480842108146302658237049009835250841238218088922049770004409037784980307049962108600922238464000000
Faltings height: 17.6453
naive height: 235.6143
primes of bad reduction: 2, 3, 5, 7, 19, 31, 43, 71, 79, 113, 137, 139, 157, 1723, 7669177, 275868873061
regulator: 39650299674.0432485340351127332231034743086492735206319743123
submitted by: apkorte
submitted at: 2026-10-31 00:01:57 UTC
last updated: 2026-10-31 00:01:57 UTC

Witness: 11 independent points log in to add more points →

(-10065374970264276, 1716384680722587506103318)
(8606991577954044, 609493523132346129207678)
(12549070919320644, 903698706895080818514078)
(17900455913067684, 1833960450704517982090398)
(-1313985754102397605134/80089, 22513020834154576383115752248886/22665187)
(-4319779856623596924/529, 21041206269367525249602556626/12167)
(-2915619757471625244/169, 1489440309219603374268096246/2197)
(-1952624672793919176/121, 1420765307891173941560565918/1331)
(5392229308150696/9, 33603479148296013262297706/27)
(74767002967620024924/7225, 410779421023332012685600541862/614125)
(993718451629454052756/64009, 22367790922259063413692595220646/16194277)

Commentary

Specialization at T = 1275/157 of the fibration given in curve#6190. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.

last edited by apkorte at 2026-10-31 00:01:57 UTC · history