curve #3425

y² + xy = x³ − 44790628100035593308549152200248056809845x + 3986160332241686982361793541175858592785562757332770282805025

a-invariants

[1, 0, 0, -44790628100035593308549152200248056809845, 3986160332241686982361793541175858592785562757332770282805025]

rank (lower bound)

≥ 26

torsion subgroup

trivial

conductor (N)

45467679786278413868196283061407028206713683768686795352562096822398494340531575288920808772153484974010

discriminant (Δ)

-1113278485902300757409951647379260907451320287915200829547152946903486009647376806151021803397838122384966844070364006400000

Faltings height

22.3476

naive height

292.5990

primes of bad reduction

2, 3, 5, 7, 23, 67, 197, 801324902916607, 890032762539245620158255255715589218981782065865354492775151344036099206453638179

regulator

28937290132424444981903433699.6055839987498836706574656534382123365760284575445504768320907

submitted by

Ritik Jain

submitted at

2026-09-27 03:33:06 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-27 05:29:58 UTC

Witness: 26 independent points log in to add more points →

(449570988722925957535919485/3640464, 4039230032640246169242503891538267259835/6946005312)
(871057103267414550010/9, -20163987411799980949139315316715/27)
(-891030518106610914110/9, 73696576360252848238338263659885/27)
(102238295257082259690, -689569382341461010257546634545)
(-300983571954755486955710/1369, -90702707159022975966827425709958245/50653)
(77631939042507037330, -988353592212371431899953550185)
(-246598486584036472310, -188697738923673055093849633145)
(2493886882889125711360, 124108591573494470147024988639505)
(20539158740058670951770610/289, 93083360522455972478507454493169389415/4913)
(1335611327068223424844225/256, -1542299181162564730025647147571923145/4096)
(1656615254084810605162, -66904090456248825409183220809913)
(44046359563774587030610/289, 4110252649162254541514338466490215/4913)
(114918757512572887890, 597102155080899543329860138455)
(-173251759461725182670, -2558487994713136372905217987145)
(7049693198520412546473250/5041, 18516033909130949944167498258915062945/357911)
(173408989678471043422, 1197325605369531191854074243391)
(-4269308094574127070974431694015201223070838/17894419628364092472201, -2501232849809156972821644372193320743096513785470415708735713437/2393736963713023883734889353382949)
(-7119765805324776986031226039817217316569756956676733304250844484798040161456194828133223487296041367635116714307955509/189872507495452353959261794035599271188272017935279270367188104241925244065882450314044679002654116, 6198545390382007577724045721618126853438115590577898286214130015532212196557357732249042457573093109326642293814736132241396858491637125016629668641636233170619697359820320851237/2616333660804418807285318878648025559238227893022174547352676287963034310761419257369627435784412534291238016767888632392908306290990254002692085336)
(-255104820016010839477686341204393262271175280/1273966562748542887853281, 3191376758537705316835634410043039506467688080146145615936959551425/1437927680612662412250940460794721071)
(52178411720571360265181823571810/482431652329, 213759711440540564155104987360325472394210111235/335084000053110517)
(-1906752727939981756870547678/14295961, 148891318527664314783755514475433857836667/54053028541)
(682573626172764114508712146121542/9987312793441, 35206333145400460930186139445388062980476908883457/31562614989040582511)
(-841334329247295655496861503286915838044714341746761119504401980159264575458604094873126964170999418056192214321230/15539103170950401029679392816831171937452897252056138368758900503678744745450216930105132495169, 4843588663030603401458779701853138018130057205077075517540616151985730758119216333772792643332100423223647040191729514178514915512972498357991101152762885990442404864427305/1937041499671473626378163693344127933602315152734686532078662639273188558006120142191125832768109458050430744396265296625735965186498754748447)
(-10947344166879564028180219398045235646490866715044750/44753837304575644908805079672329, 165634573493250450320547241206420986095361267198539474073122383921097784446835/299395603138402791933727924107149446551107605733)
(-7372607960851022710989936660301481039792630/29894094263648284041969, 925508881379597267208760056082060022625277271803484865549458495/5168661602993397661363267887658953)
(-22343877637902315049876792425626562626570051678807521868727393594607390120557820679798222489270/131478809539032807196579204159000806011351207230449238031495967573612389841, 3899379330471103862738061508399775251585362967911243256243871271338725017677719761891660791893072559881585446033695050558244793832904298218095/1507591376961629915336508801551453416688138244491193111289258861359375919278857793166137542277962672153194820889)

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