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curve #4363

y² + xy = x³ − 185329799649605x + 1186467616736654585025

a-invariants: [1, 0, 0, -185329799649605, 1186467616736654585025]
c-invariants: [8895830383181041, -1025108034204215136233161]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 1570867223266770
discriminant (Δ): -200733705850059797418994503096888385910400000
Faltings height: 7.2160
naive height: 110.5737
primes of bad reduction: 2, 3, 5, 11, 13, 17, 109, 197609021
regulator: 1188.35653589162559601808164787202306384889483193
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:06:23 UTC
last updated: 2026-10-17 10:06:23 UTC

Witness: 5 independent points log in to add more points →

(-15699350, 15061510495)
(130446760, 1482074939695)
(9167910, 16056200895)
(7705570, 14690375335)
(30250995/4, 117930450435/8)

Commentary

BASE torsion/torsion_Z5.tsv.gz:1315 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:06:23 UTC · history

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