curve #3550

y² = x³ − 240005545330536236099527000812x + 36700078011396568556186592483815843659153620

a-invariants: [0, 0, 0, -240005545330536236099527000812, 36700078011396568556186592483815843659153620]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 2346409587597899767985215535053737912784685398154665256151005994854441862326088
discriminant (Δ): 302938374686068516641134144421785144957100623373701509574062824461662494315365873627688192 ★ record for rank ≥ 23
Faltings height: 15.8862 ★ record for rank ≥ 23
naive height: 214.5650 ★ record for rank ≥ 23
primes of bad reduction: 2, 3, 13, 53, 67, 83, 2423873, 3509048332575999972992242067725795185834441969977070129230866937
regulator: 268172257115121960118049876.441196630132975129550623770898003048044757389414307762254
submitted by: Matej Jurasić
submitted at: 2026-09-28 08:36:16 UTC
last updated: 2026-09-28 08:36:16 UTC

(1749904236041569/4, -31424714514993214670671/8)
(1669087838575218, -65467130133148629843906)
(564867169629642, -9020186888544185549598)
(484000111162473, 5823860361757813076481)
(65956194463548646/121, -10962458060638929818421682/1331)
(1172705320546041, 36986388666274658891943)
(54843569824841418/121, 6104086725498074539310214/1331)
(775069726423716, -17784517712200695840618)
(-2929552970331516/25, 993850880249925470881602/125)
(800340962524281, -18901553797233486305433)
(70068636471102, 4497468915994179616998)
(358159141133770089, -214345146372324251308416639)
(-287881569926828838/1849, -666597263477829506423795142/79507)
(-270310681932023, 9045723646275983586127)
(25148902110969009/64, -896445727576949819491479/512)
(4151169394060372, -265658066126742392007398)
(605648875434873/4, 15659437347521502031341/8)
(-61852251082749739086/116281, 147633974509796651454855430554/39651821)
(-476154729379536074034714/1129296025, -301068472301380908013139358582152466/37949992920125)
(-12021384477308391528754163666/22444503178969, -362121614908960545501067801562520274140914/106332247814065912547)
(458568175648095310695732/2725988521, 148354124126359897759941887126112738/142326586669931)
(333163294022097270166664638926/648803680140625, 115517537543592619858611574560051986653346826/16526084039161947265625)
(2729440579852309413186006/7103624089, 658065708124110531130463164142271378/598714749093187)

Specialization at T = 45/11 of a rank-17 fibration of X1008 (2-neighbour of the one in curve#751).

last edited by Matej Jurasić at 2026-09-28 08:36:16 UTC · history