curve #4152

y² + xy = x³ − 1119988002679795605079798078674871712695311x + 455080836353385315145047140078151435876514415822516122283621241

a-invariants: [1, 0, 0, -1119988002679795605079798078674871712695311, 455080836353385315145047140078151435876514415822516122283621241]
c-invariants: [53759424128630189043830307776393842209374929, -393189842609324912285401368163715785880874200732318520416362814617]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 2273576193560163584381385053446958622052889403791631448865441676495095120189598470991013093470
discriminant (Δ): 445921328612897794323325120666241150736247563015998382694632659679993137730509269829032554375560414413677631943675716790476800
Faltings height: 22.9810
naive height: 302.0793
primes of bad reduction: 2, 3, 5, 7, 11, 17, 29, 79, 97, 157, 5440594613, 200950563217, 7476881595398278306301002802207157381284878679576059417973
regulator: 65194703238651926316571306.94643932971960545368499848754962019460092646746628908685205608
submitted by: apkorte
submitted at: 2026-10-11 05:03:32 UTC
last updated: 2026-10-11 05:03:32 UTC

Witness: 25 independent points log in to add more points →

(489050016006283808256, 4931200463970535784486213610357)
(171675855854326225494, -16366602310501519743640249217427)
(499082354030252268126, -4519691953410110690108543981643)
(642326646562834989606, -834318763381164680903907476163)
(570709601353129263876, -1333581517551050288691236168643)
(-179634973651206499674, 25504377278555000763337824131517)
(5962189567913004101526, -453563284064041126850101269545043)
(1080119239075046090052906/1849, 32657472313080729101851861043974611/79507)
(637769127013209158994, -446445109244416489520084018667)
(-426870169211659020030, 29246996696205475655393520821301)
(528101685868244582406, 3300954035297756198516286752157)
(207098264858668443005958/361, 8026206428777850934389562701739743/6859)
(697032768216134128860, 3615125309350029577127638798029)
(-1138687558930321178544, -15936257329929980506903813122213)
(280992013036405510158, 12749874586758194905128204344205)
(567279482208504624486, 1512801826824732575807301018237)
(581675550885678382830, -647343468854470919511691664571)
(728966171432373051126, 5100394869543382048837649003517)
(654062034556728479070, 1531364002607893393931748382701)
(-81356360592431704314, -23359377089439601609927791300963)
(5199460554739343107494, 367690076195488014979916430607773)
(514890449812757621376, 3861791949610620308872512192267)
(641443916558601543798, 770477833163073441863873521917)
(501818153018807963826, -4406711329612637542087863470343)
(4392869866544861902128534/6889, 248468635489251522952213594991748159/571787)

Commentary

Specialization at T = 367/195 of the rank-17 fibration of X1152 given in curve#3856. 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 2026-10-11 05:03:32 UTC · history