curve #1802

y² + xy + y = x³ − x² − 1444491707528591356856089186460491195711268950880x + 559921583779625421248683584939561762456224290170437461555851482041439747

a-invariants: [1, -1, 1, -1444491707528591356856089186460491195711268950880, 559921583779625421248683584939561762456224290170437461555851482041439747]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 22849025621835725749454395101099261802452962113733638743150
discriminant (Δ): 57459587060568346526411497511414303188663056470735043434542454028394906031620087025662290300911169325668216298192719212022528766515354009600000000
Faltings height: 26.6889
naive height: 344.2891
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 31, 53, 59, 73, 83, 89, 109, 131, 149, 191, 239, 263, 811, 4903, 6967, 12379, 362707, 945577
regulator: 5868464385890.1914216628033196847720602717481849275530270032791
submitted by: hdeping
submitted at: 2026-09-25 15:05:02 UTC
last updated: 2026-09-25 15:05:02 UTC

(158850932500649609134809, 578334775816714524616276221704042845)
(351104017200784386392209, 309897966944945116194624198332593845)
(-427722660290928813983135, -1048576645526111528109185629948786727)
(954500781939375762742909, 225326008863345220543071618783370945)
(423679598259676591990909, 154829810959547852593332987635966145)
(1535808449095818094207905, 1401421444080498380369785533616999513)
(444801887422056021535383, 73569216148613399817347986859758945)
(-1206006015871044278678751, -740210245609217615143269452335454375)
(-192562292438693523617091, -911556889640548767064630159456313855)
(10508879668527356682921249, 33851800053181168926568362825476385625)
(951514410733369555670349, 216676520921276805299703311439049825)
(-7355680099955426717481581/81, -605705671933225602690651446390633849125/729)

Rank 12 with torsion Z/2Z x Z/2Z induced by a rational Diophantine triple (Dujella-Peral, RACSAM 113 (2019)); witness points from the paper.

last edited by hdeping at 2026-09-27 08:23:37 UTC · history