curve #3335

y² = x³ + x² − 1834590106026958306720x + 66141175438074109110482837181200

a-invariants: [0, 1, 0, -1834590106026958306720, 66141175438074109110482837181200]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/4ℤ
conductor (N): 1185557421935264818440
discriminant (Δ): -1494669034408399803847005284005580359490923482072604670593193702400
Faltings height: 11.3865
naive height: 160.0618
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 31, 67, 89, 193, 347, 2039
regulator: 7534307.037734179442494821425851534602589587876112350
submitted by: David Renshaw
submitted at: 2026-09-26 21:01:44 UTC
last updated: 2026-09-26 21:01:44 UTC

Witness: 7 independent points log in to add more points →

(42061619504, 7961778288852420)
(45860199379, 8857637801700870)
(777830275360/81, 5124274585669179460/729)
(-24724908877, 9817657035952194)
(-3455199993097/361, 62422022620480451604/6859)
(1634347500896/25, 1877491518420156756/125)
(119853220791440/5329, 2342400848500524387420/389017)

Commentary

Rationally isogenous to curve#1830 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 7 carries over. Torsion ℤ/4ℤ.

last edited by David Renshaw at 2026-09-26 21:01:44 UTC · history