curve #1945

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y² + xy + y = x³ − x² − 588811743515389824718744124832117x + 5246068405024047957466483053077815196833217996685

a-invariants

[1, -1, 1, -588811743515389824718744124832117, 5246068405024047957466483053077815196833217996685]

rank (lower bound)

≥ 23

torsion subgroup

trivial

conductor (N)

251450984381664120737100844757698163795925780997158749741916350986285162243541215051406

discriminant (Δ)

1175825516109651851573344884012240925173250350155977375550325150157364714074577152812212150171041792

Faltings height

17.7672

naive height

237.9806

primes of bad reduction

2, 31, 47, 71, 89, 263, 465158816485076251, 111624218667119955062911831025876864598571330741310879984557

regulator

1445200344934895895684305.31790886929150064572660434138588037708741624232437159931608

submitted by

Ritik Jain

submitted at

2026-09-25 20:01:14 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 20:04:09 UTC

Witness: 23 independent points log in to add more points →

(11212288551075830105390181239451515860723295498337815/992925844378392834779181100700752201, 190330499129143116349232209810234119911028552589307797105597277414073157747504/989407555131701180194950365031451266066549887596037051)
(1170264534381883711/225, 5145362617291761447336535664/3375)
(148227889969467127/9, 3410268773299941179543728/27)
(510785284194458941999/18225, 8070010562088922304291734443248/2460375)
(667135016960566627/36, 180529843593751530790447627/216)
(28237765939428101/16, -131354367157586082153663841/64)
(65930819408721981327/289, -532425739251475826611470177968/4913)
(29198740047002260841491/2732409, 1885391261424897810403499075773780/4516672077)
(-9234584252105992435/361, -12958192467250258797492711214/6859)
(1995906581506281894319/178929, -19442987831744113413714071768848/75686967)
(-26685332656437003, 1398532827248614883274500)
(5258426322611231, -1515007008984363547134128)
(1880819856100117647655/301401, -222906794881328025650020853700400/165469149)
(22176006287832429277/1936, 5656234413172340082028349655/85184)
(40931795240038219039/2025, 115369299560218853230641100072/91125)
(-2653992282606888958266449/186295201, 8334254497400110631463138818977838288/2542743198449)
(172950866255588168503465423/15258919729, -317384827323805803896470895730144489360/1884888577364183)
(-3093558553009151768578045574725606985/140452817941573330561, 4567587001923853098970473105669970382321167322149058520/1664545555498317471563530383809)
(38796347087454142830315948584270583/4115466016888777321, 6095908413534583143618994649007099517309023255623728/8348885977337380236337228619)
(21894976796307558601792124803794708839095/2269613386273174070502409, 2328072588069515727551357240913910091540796554207496304700400/3419226151077932452183594569964019173)
(113804815926080951941340788960390123267058999/10373660522309649802714314601, 345316860755285738755066082342723422144297122844506759391722438640/1056569445691951753147316411565272484593099)
(6927732919792937723631230095687429133286015/993025248327157057883080609, 38041045001740397022502052283232110537450730218628931656350395280/31292512637407335538481450458933411188977)
(-333731048738079600392558679283614593705/14101905912603239591721, 4076734001066546705397949180437063544663428622618317864880/1674621717617368065132520763471019)

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