curve #2006

y² + xy = x³ − 9739872505237802121075026235x + 369975493857777571943772978374733893742225

a-invariants: [1, 0, 0, -9739872505237802121075026235, 369975493857777571943772978374733893742225]
rank (lower bound): ≥ 14
torsion subgroup: ℤ/2ℤ
conductor (N): 226358749368754196185387455802611568740743010
discriminant (Δ): 1378767061590717729092957015138634096840454949409005399919763585107600000000000000
Faltings height: 14.7118
naive height: 204.9517
primes of bad reduction: 2, 3, 5, 7, 11, 41, 127, 137, 193, 197, 211, 269, 449, 863, 1153, 1289, 1697, 6833
regulator: 313162372817212984.760063632930555763956534481711322401746509535525
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:58:17 UTC
last updated: 2026-09-26 04:58:17 UTC

(78417888945952830/1369, -170300418620506116002355/50653)
(56006230598331870/841, 3150785686959770670312885/24389)
(32037799318964430/529, 575482277365381886362455/12167)
(167819630431095070/2601, 13362913034296487370480715/132651)
(293400927044281230/4489, 33748048979721487833078795/300763)
(4099581887693505/64, -48331477097427185580795/512)
(41394979495488830/49, 8367055489530877579871495/343)
(11872370618061559230/27889, 39894023190193428532106264295/4657463)
(99206210899692876030/142129, 978732883866150434914536708345/53582633)
(3514930015808419222830/60637369, -6033133578693219054395860588605/472183192403)
(52281217924749986670/36481, 377149659883514479920982578015/6967871)
(288785473723222957630/5049009, -22026799506996864824251397305/11345123223)
(17111603695496186197070/292444201, -100162139549909561877618082547035/5001088281301)
(455027681361782759614/6365529, 3171880633891298709613990897219/16060229667)

2-isogenous partner of curve#1977 (Dujella (2002)).

last edited by Steps Unbounded at 2026-09-26 21:37:40 UTC · history