curve #1872

y² = x³ + x² − 37244113713654521144652465881991658490660x + 3418191096359858638496071482246769986373727295968405811851904

a-invariants: [0, 1, 0, -37244113713654521144652465881991658490660, 3418191096359858638496071482246769986373727295968405811851904]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 57608397914326918614081909678741668061379318755784095402421015300159648972424136509090376792
discriminant (Δ): -1741120049898811122934124112659780170935040515507935195062893075857335328687618881445877050147708690195618760997475193093888
Faltings height: 22.3615
naive height: 292.2916
primes of bad reduction: 2, 3, 7, 11, 13, 23, 29, 31, 41, 89, 101, 113, 797, 34679, 4380528870842104524555059605672046110274694413816043896624388005933
regulator: 6489692613557759718556638.3436041587208771616874927519645354221385919906352641563968067
submitted by: Ritik Jain
submitted at: 2026-09-25 17:21:54 UTC
last updated: 2026-09-25 17:21:54 UTC

Witness: 24 independent points log in to add more points →

(-173753540963785281308317634/896809, 1557056871524205543672596785877718330666/849278123)
(1420793505819255610189/4, -47330707474895866664583456278763/8)
(74755578516237586590217/1024, 34184320021409940997303553144955675/32768)
(-531009720826506455387/4, 19633300770448818053541656723007/8)
(390864568681734556159072/5041, 357291911386504838165684799412892016/357911)
(-92824974429181375094, 2464863251063422707230625378486)
(-151337822388967103160761/1369, 125966797763568473318771187774893142/50653)
(5992202869250387540254/361, 11486630252398965895448656262305482/6859)
(32781432126510984048610/49, 5718250314429507428628802802225886/343)
(3144742829482139812831181429315195583115279421371/2321803123940860728086563969, 5523680145493861243244462287597498437271352019637926100125451985008539804/111876297925439366383665066495559555951297)
(42988200639560700310860934/289, -281853567063825500016631175005038132282/4913)
(-136245106251409502918, -2442015222038231228463661246374)
(357108275199891057844, 5971491785286064526618216472528)
(-213068768873161239319904/2809, -358753992670735624533174799779039456/148877)
(7657124639668792088951017/15376, -19848216302625988029723144700118501181/1906624)
(-179260810014997283468, 2081863516757749149302680281024)
(119598231676797186244151599/1129969, -977226348979570012725424340961558069858/1201157047)
(21665267119501189471, 1619091334520428603869396748386)
(26771964224512607092510/529, 15689949645120861049994652046313634/12167)
(234234529295570530533730/2809, 140634486301125112046348803934629446/148877)
(25565111572190211585622941389229925416860086/381884478786575395894561, 261186748556501403271533657549638189815398602161531735848139205226/235992396782942557909692180584923441)
(-9201132720110876206939577899256126/133364687979769, 3663907474706912941014240827395083413681458174023258/1540143828172109068147)
(50978453123696263667967243766/531717481, 10466330468580332291224248270070847378257506/12260873394379)
(3337823818049089157949516876114319/280368735966225, 8099273406861000816648433551849340567819792852042978/4694554394296704138375)

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