curve #5746

y² = x³ − 6338301011743932x

a-invariants: [0, 0, 0, -6338301011743932, 0]
c-invariants: [304238448563708736, 0]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 8927568825660922670440875293472
discriminant (Δ): 16296658133788861354615622749172617115236381028352
Faltings height: 8.1324
naive height: 120.7698
primes of bad reduction: 2, 3, 7, 11, 37, 43, 53, 113, 317, 757
regulator: 3045598174657.432024777889867174235083650225115881059514047
submitted by: The Wren
submitted at: 2026-10-24 18:38:32 UTC
last updated: 2026-10-24 18:38:32 UTC

Witness: 10 independent points log in to add more points →

(113891584, 869161638304)
(79637776, -17565448312)
(35484010384/289, -5088602962415384/4913)
(144769024, -1454816047616)
(136406126224/9, 50378452363932904/27)
(12714592081/4, 1433234929569913/8)
(222469395806464/567009, 3249193284062994503584/426957777)
(245085819317089/1144900, -3561650951588140123313/1225043000)
(454652169841/256, -306254232516673783/4096)
(9635276446389136/116791249, -247993673977699215159448/1262163027943)

Commentary

Rational 2-isogenous partner of curve#5737. Curve#5737 was submitted by Michael Rubinstein with rank 10 proved by ten independent points and torsion Z/2 in the family y^2 = x^3 + ax. The displayed points are the exact images under the 2-isogeny; each was checked on this destination model.

last edited by The Wren at 2026-10-24 18:38:32 UTC · history