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curve #4414

y² + xy = x³ − x² − 22075864x + 43047713164

a-invariants: [1, -1, 0, -22075864, 43047713164]
c-invariants: [1059641481, -37188455787045]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 55895061045198499766014
discriminant (Δ): -111790122090396999532028
Faltings height: 3.1646
naive height: 62.4940
primes of bad reduction: 2, 2309, 12103737775053811123
regulator: 67890696.7418691483323234924419213087585997624425798262518913
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:22:53 UTC
last updated: 2026-10-17 10:22:53 UTC

Witness: 11 independent points log in to add more points →

(-2166, 285158)
(-2130, 284618)
(-1475, 269808)
(-1324, 265150)
(546, 176240)
(2895, 56818)
(3141, 66904)
(3158, 67842)
(3159, 67898)
(3642, 102800)
(3938, 129070)

Commentary

BASE records/rank_11.md#23 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:22:53 UTC · history

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