curve #3482

y² = x³ − x² − 19613351862529095444140500x + 32417180218045560823093188132585778852

a-invariants: [0, -1, 0, -19613351862529095444140500, 32417180218045560823093188132585778852]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 1345431868373595535776246698855160
discriminant (Δ): 28898407655395816517616685896391049620814027107083576688153334926485156000000
Faltings height: 13.4429
naive height: 186.3284
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 37, 53, 67, 97, 109, 139, 151, 167, 211, 269, 271, 463
regulator: 357847001.9149951820983336354747538686802009069206316608379
submitted by: jesper-petersen
submitted at: 2026-09-27 09:16:27 UTC
last updated: 2026-09-27 09:16:27 UTC

(3013492508709, 823668580909281250)
(-2220108328736, 8063392356960348870)
(-5007963311516, 2245423496309241150)
(3738925387308, 3369401164461607990)
(32962572923769/16, 55587408935053070075/64)
(-7591682767, 5706669617723376120)
(118751937876781/9, 1228664171759974412050/27)
(1594274253771181/484, 20066760097614444730425/10648)
(294657034603858, 5057389897199959832520)
(-239839870368159/49, 1145407301143481615800/343)

Dujella - Kulesz (2002). Source: https://dujella.github.io/tors/z2z2old1011121314.html (curve entry 73).

last edited by jesper-petersen at 2026-09-27 09:16:27 UTC · history