curve #4090

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y² + xy = x³ − 7399395255648189797319275080085394168375x + 239898227386207938563037636274941193287416724179122935568041

a-invariants: [1, 0, 0, -7399395255648189797319275080085394168375, 239898227386207938563037636274941193287416724179122935568041]
c-invariants: [355170972271113110271325203844098920082001, -207272068461683658918997274199955860665735037496528364710910425]
rank (lower bound): ≥ 27
torsion subgroup: trivial
conductor (N): 284216011255408892412509641133766698205691875129598201518473831484832026761852624857187143593310763802
discriminant (Δ): 1065877380544049069044256405290585906937897463646381752654841066750183388400514807940342781567628358370528452088710971392 ★ record for rank ≥ 27
Faltings height: 21.8162 ★ record for rank ≥ 27
naive height: 287.0203 ★ record for rank ≥ 27
primes of bad reduction: 2, 3, 7, 13, 31, 43, 373649, 141475287469601533424653, 178551308428745055322181168501, 41373122744267219567864029620183855337
regulator: 63912907383360147483155683156.294002597780649280412812680027897643314516911446995378502955932
submitted by: Matej Jurasić
submitted at: 2026-10-09 11:08:11 UTC
last updated: 2026-10-09 11:08:11 UTC

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

(43391449787758794204, 22933353319119892588931210751)
(64617757185372690390, -177691894274619554317857614091)
(104018903023715644902, 771815215307379762793113511749)
(-23789865153323084970, 634401123709712495408386836981)
(37548610389943611558, 122478299456040971534038562133)
(38496424611800225238, -109994060646151523317809245451)
(-22691896242491042994, 629380629414986221033039376493)
(-93256007655205085754, 344845407359744402716993463061)
(40220051245263464694, 85768516108190842444946858325)
(319335145030803301974, -5517353702860259745464344118859)
(43683994045289728158, 4987629401105022067233779109)
(72179564282089272918, -286113012579995140089669121611)
(11619978962363167326, 394317619671016903148133062181)
(292460636846756420070, -4805306189338302953961907594539)
(96351970636058507190, 649195593850221458194439093301)
(272528391946136286534, -4297034624077890219869868194139)
(-69361565029707468126, 647635330329344318521100467185)
(-78180187712054626794, 583554580208482212994534325493)
(1374372688947965616678, -50853941240474041931605867127931)
(2001077681781857863758, 89433619430087430499241811948909)
(122305854074261872770, -1079095979964838593839901581139)
(646355617722664062892/9, 7584425343313730312807625991751/27)
(4068773550892738676310/121, 227076687001990499168034782338719/1331)
(582752965718661351789/16, -8754978057775906189956733319295/64)
(3004688117455590894902, 164635306368584527038742166841749)
(569565926921296351624830/10201, -29501890458193614746659350099120711/1030301)
(2141144585518088610874134/36481, 615084967711644197526846243724290891/6967871)

Commentary

Specialization at T = -684/1063 of a rank-16 fibration of X1152 (two neighbour steps from the one in curve#3856).

last edited by Matej Jurasić at 2026-10-09 11:08:11 UTC · history