curve #4762

y² = x³ − 14752493461692x

a-invariants: [0, 0, 0, -14752493461692, 0]
c-invariants: [708119686161216, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 48363569630503379882556192
discriminant (Δ): 205483174490329023755553842685251346296832
Faltings height: 6.6166
naive height: 102.5809
primes of bad reduction: 2, 3, 7, 23, 71, 113, 281, 1129
regulator: 307222989.497645174191965739370305318630605517613749152
submitted by: David Renshaw
submitted at: 2026-10-20 21:28:59 UTC
last updated: 2026-10-20 21:28:59 UTC

Witness: 8 independent points log in to add more points →

(-3136803, 3925683243)
(-22862, 580740524)
(13821712, 49361840632)
(-2353765564428/1274641, 6586039283570524548/1439069689)
(-14991144027/6889, 2669588449052391/571787)
(-475712496/841, 69685038798984/24389)
(-22862/9, 5226756164/27)
(64336441/4, 501112753037/8)

Commentary

Quartic twist y^2 = x^3 + a x with a = -14752493461692. Source: Aguirre, Castaneda, Peral, 'High rank elliptic curves of the form y^2=x^3+Bx', Rev. Mat. Complut. 13 (2000) 17-31, https://revistas.ucm.es/index.php/REMA/article/view/REMA0000120017A.

last edited by David Renshaw at 2026-10-20 21:28:59 UTC · history