curve #3814

y² + xy + y = x³ − 1208324064247212118689505701813x + 507340853630200446935827633415633644217833588

a-invariants: [1, 0, 1, -1208324064247212118689505701813, 507340853630200446935827633415633644217833588]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 320325488024303410503048732334758611849984584750604941844180926857858030
discriminant (Δ): 1714910181880885463364393077713956069714325528789474229680570566013046195237332855740937500
Faltings height: 16.1380
naive height: 219.4140
primes of bad reduction: 2, 3, 5, 7, 13, 23, 41, 43, 71, 136307315309778418523589193892149921082248499305004998984091
regulator: 317229832420698756913.8971558893479584034920686349139881303738883985512131379939613
submitted by: 7fff-zip
submitted at: 2026-10-03 04:55:45 UTC
last updated: 2026-10-03 04:55:45 UTC

(1404242554725323, -39743964744475043953512)
(-2321545908726130291/3721, 7243363743245022675135140910/226981)
(586440112851854, -644165348728833563490)
(1527359017959946154/3025, 847758736098906482598087573/166375)
(-1025288478269688061/841, 316567310243718050419416840/24389)
(8601680311654391/4, -708943474623730120765695/8)
(-5882065019472464/9, -861418845270332275110055/27)
(-1263232119578896, -4233811057136879179365)
(24897288858564098174/36481, 5248134549609894525580093485/6967871)
(-974842280188154431/961, -782109986712688291250463840/29791)
(3354357664916319461/2704, -4258829886191073979188825105/140608)
(178036779723815939/121, -58244076890591616304376400/1331)
(517056871565729, 4560988075313917709760)
(-1262761879894111, 4428011937440117776320)
(1412090938539440416169/1515361, -25748899838378257861796673750840/1865409391)
(2549509204447404316661/9409, -128730456289708371494715954931020/912673)
(641218391870406754, 513462011561438350198973210)
(563862513249787, -2299388019633285592480)
(588823953752429, -63261997655521869540)
(27598852393503596/49, -800432014808666300323320/343)
(575018394975947, -1630923552542327207400)
(27996725546798906/49, -639322459756372394485650/343)

X1008, T=-46/53.

last edited by 7fff-zip at 2026-10-03 04:55:46 UTC · history