curve #4296

y² + xy + y = x³ − x² − 13957520891x + 528121873348746

a-invariants: [1, -1, 1, -13957520891, 528121873348746]
c-invariants: [669961002753, -456294283748804385]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 5685053598081
discriminant (Δ): 53533571806915384243339380681009
Faltings height: 4.8075
naive height: 81.6915
primes of bad reduction: 3, 11, 13, 103, 181, 313, 757
regulator: 437849.94975437774680894346566650465795351398098998
submitted by: The Wren
submitted at: 2026-10-16 19:01:52 UTC
last updated: 2026-10-16 19:01:52 UTC

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

(2615439/4, -4166827781/8)
(89172731/196, -816248637513/2744)
(1986069/16, -1707103435/64)
(228922409/1600, -2450028534903/64000)
(17559929/169, -31156442829/2197)
(483817149/400, 10587834679417/8000)

Commentary

Obtained by a rational 2-isogeny from curve#4086, 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 19:01:52 UTC · history