curve #2017

y² + xy + y = x³ + x² − 6417061776794472069990610896x + 197857322114823898105377784162593105601554

a-invariants: [1, 1, 1, -6417061776794472069990610896, 197857322114823898105377784162593105601554]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ
conductor (N): 8969825157965317726623690832455919395
discriminant (Δ): 24696184751330735348142655798285768007676350715055583604459488643821205292798575
Faltings height: 14.5364
naive height: 203.6999
primes of bad reduction: 3, 5, 13, 23, 37, 53, 61, 101, 107, 197, 1303, 1933, 2953, 3673, 4783, 60101
regulator: 20548616588604.2753725116194246053836055066952874672171566713
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:01:08 UTC
last updated: 2026-09-26 05:01:08 UTC

(60060325355974501/1296, -48128115374208608868035/46656)
(22053501629507933/361, 1261502571979398349625676/6859)
(116472667987197191/2500, -498262126068055502260389/125000)
(185160259040567/4, -2310286569537736269/8)
(50930593158653, -56059945354222511718)
(18219366641107730821/383161, 3649447676004129186075227942/237176659)
(9259306837301869/169, 227682849956265963687446/2197)
(13917238495283857/256, 402794823439555052019281/4096)
(291329914072093933/6241, 2496765503769635056679648/493039)
(34378746289373593/576, 2291291627090659539079343/13824)
(959421500531331936853/1792921, 29402156774546231942553995755358/2400721219)

2-isogenous partner of curve#1245 (Dujella - Peral (2023)).

last edited by Steps Unbounded at 2026-09-26 21:40:18 UTC · history