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curve #1253

y² + y = x³ − x² − 193153379648x + 32356411177781898

a-invariants: [0, -1, 1, -193153379648, 32356411177781898]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/5ℤ
conductor (N): 117307241825
discriminant (Δ): 8922328967249110243842613069709125
Faltings height: 5.3284
naive height: 89.5739
primes of bad reduction: 5, 31, 149, 431, 2357
regulator: 4390.936174034353577086345412833375952774903444
submitted by: hdeping
submitted at: 2026-09-24 16:28:00 UTC
last updated: 2026-09-24 16:28:00 UTC

Witness: 4 independent points log in to add more points →

(-59628, 208953942)
(21277293343/15129, 2967168407132384/1860867)
(477406512/961, 7236360723527/29791)
(53033192137378/113486409, 254009409712649360594/1208970715077)

Commentary

Found by a Mestre-Nagao sieve over the Tate normal form family y^2+(t+1)xy+ty=x^3+tx^2 with torsion Z/5Z, at t=2357/-149.

last edited by hdeping at 2026-09-27 08:28:54 UTC · history

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