curve #1676

y² + xy = x³ − 2349255761373715511008814441060715030878753465x + 43941095751430698889503351013858456493493657978751558977339647439225

a-invariants

[1, 0, 0, -2349255761373715511008814441060715030878753465, 43941095751430698889503351013858456493493657978751558977339647439225]

rank (lower bound)

≥ 27

torsion subgroup

trivial

conductor (N)

4630825187463464945352863121366491149784801732582815693910529024216898563340055137773647064132848889142770

discriminant (Δ)

-4319076212250604011475370536184346362122203684406897565418065887787004549297552775628052367484129423060429908770836925498211081420800000

Faltings height

24.8953

naive height

325.0301

primes of bad reduction

2, 3, 5, 13, 19, 29, 37, 61, 71, 101, 103, 109, 6240407, 1233180803, 3961747351, 3889920537362469928356372466643128585828054313370011450122443607

regulator

59102561670592503059003219209.338239244738981984895620141556674623082817134518687768143721144

submitted by

Ritik Jain

submitted at

2026-09-25 04:08:29 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 05:30:30 UTC

Witness: 27 independent points log in to add more points →

(305877619605368860418680, -167163418398857918390689866760652165)
(160933879579358016101234290/9409, -2701693900126471282640493396017247773045/912673)
(159572136179381880159670/9, 75705680587237321056228033221188345/27)
(3554394750521023425977850, 6700517074542938351891731772470313715)
(35018737800432997080730, -2148725786836409514226947134978765)
(33923126455629382202650, -1812456992288941936190408979355085)
(2640786115238710426558499370/137641, -124357628498339411682943345952215430507055/51064811)
(25195609911063093071902, -863023648153680846053464825922453)
(29384202808307298073720, -530406104132992512863032297667315)
(338578530889943912493952390/3249, 5650114428386109521827597791117743642615/185193)
(-532346055649634476262058020/10201, 5091294898992763291634912800503949594535/1030301)
(24506233262274135201790, 1042611372208428254816428175250475)
(27163107801996386397970, -412170219276885978882530802884405)
(517509628521943355682826/25, 255588621885289407127950385157865959/125)
(87362706231135918119665630/361, -801307597759450426607315342047791579335/6859)
(-189961348223537869152590/9, 247640737906296953851622552022222425/27)
(67510537179804004028470, 13893613816751627819019253503237595)
(284902168538477931545928112330/8462281, 42704600321389798639186329271787750036238815/24616775429)
(17237713650641677857423637018/452929, 947272550244304993780020708331036555058899/304821217)
(1047221290349662463952462927371275758178030/42439924444223562481, 275997826239754551190688830569192285114662976389916292567990685/276478842810893279420485666871)
(3289271871157626439389611891444954961601585471171178835339/113607169755245337186573100472952100, 16853281097551465774501592297772117188883434888022126226192530654293077227467285209233/38292049432398864103506034984482228443436872647319000)
(8539440259471732110736054/225, 10374254446024777955695531073423194037/3375)
(-518790140503371876103665346875942234080/10808067710888449, 7630092113346086079007748943127877229422769262144555242955/1123626789805702277889793)
(-732274862234609733138526397880/20097289, 811695687371747203602536981519077930986655695/90096146587)
(12808531578030836707751036179915/428407204, 5805068779084176338713319349787975538234696695/8867172308392)
(7799558053780749882079480/289, 2175821900152332534167115305533271435/4913)
(-137934957242352998167926545962232305835654/2464049180532870225, 688943549877395599279363080249943611236892982682264631347461/3867889493069419553412078375)

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