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curve #4510

y² + xy + y = x³ + x² − 393303086x + 2225243339858

a-invariants: [1, 1, 1, -393303086, 2225243339858]
c-invariants: [18878548129, -1922751834748433]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 104743458900273135
discriminant (Δ): 1754243053207782527446184025
Faltings height: 3.9366
naive height: 70.9839
primes of bad reduction: 3, 5, 19, 47, 61, 103, 199, 709, 8821
regulator: 22871.1425895865137241482852199240176672923562755214387
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:03 UTC
last updated: 2026-10-17 10:33:03 UTC

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

(25196, 2870414)
(4334, 773783)
(123711, 42913864)
(-288787/16, 119357657/64)
(16076, 231694)
(-21164, 1044989)
(-9321/4, 14160707/8)
(-8833, 2242768)

Commentary

BASE torsion/torsion_Z2.tsv.gz:635299 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:03 UTC · history

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