curve #4295

y² = x³ − x² − 5351085089x + 149090775069729

a-invariants: [0, -1, 0, -5351085089, 149090775069729]
c-invariants: [256852084288, -128812888547740160]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 5377165292352
discriminant (Δ): 204016524837476185707106074624
Faltings height: 4.4351
naive height: 78.8153
primes of bad reduction: 2, 3, 7, 137, 193, 337, 449
regulator: 693682.73777603233343908203632463241027034981100740
submitted by: The Wren
submitted at: 2026-10-16 19:00:23 UTC
last updated: 2026-10-16 19:00:23 UTC

Witness: 6 independent points log in to add more points →

(20136097/144, -79845170185/1728)
(20721637/324, -48252214675/5832)
(56081, -5037120)
(185253/4, -6199725/8)
(27739553/529, -43322169600/12167)
(46770981/676, 184384901085/17576)

Commentary

Obtained by a rational 2-isogeny from curve#4087, submitted by jesper-petersen, whose source curve was found using a Tate-normal-form discriminant sieve. This isogenous curve has the same rank and conductor, with torsion subgroup Z/2 x Z/2. The six supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 19:00:23 UTC · history