curve #4527

y² + y = x³ − x² − 7431287259945094540x + 7726194963844170252728077612

a-invariants: [0, -1, 1, -7431287259945094540, 7726194963844170252728077612]
c-invariants: [356701788477364537936, -6675432446621152367492871829400]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/5ℤ
conductor (N): 22440710685096689557
discriminant (Δ): 476834251841812285639531696506050747692958325631691834677
Faltings height: 9.6920
naive height: 141.9703
primes of bad reduction: 11, 13, 17, 19, 23, 31, 43, 47, 337164781
regulator: 20656.548518170829340550941775258682370394698423437
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:57 UTC
last updated: 2026-10-17 10:33:57 UTC

(-448884132479/144, 42336536675013575/1728)
(41313038893/36, -5753377263080555/216)
(90825544456, 27360154966106748)
(2706055621/36, -18287462541693167/216)
(21176948761/16, -925389961129941/64)
(558918695105/16, -416616161008305433/64)

BASE torsion/torsion_Z5.tsv.gz:2091 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:57 UTC · history