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curve #4392

y² + xy = x³ + x² − 5157621363938497x + 203250515623581340378681

a-invariants: [1, 1, 0, -5157621363938497, 203250515623581340378681]
c-invariants: [247565825469047881, -175608447355517969105039429]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/4ℤ
conductor (N): 2011020983594216490
discriminant (Δ): -9065570038147322479624538362044180277072963314900
Faltings height: 8.0964
naive height: 120.8606
primes of bad reduction: 2, 3, 5, 13, 79, 97, 101, 809, 1277, 6449
regulator: 3524800.102782854387365532361112416231438998603403720
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:21:26 UTC
last updated: 2026-10-17 10:21:26 UTC

Witness: 7 independent points log in to add more points →

(-180142737/4, 4693566615587/8)
(-33813563, 582242890894)
(11674022123/4, 1260947477060677/8)
(-23862615697611/354025, 104198692671858646247/210644875)
(-7054497063/14161, 764512563774346871/1685159)
(397523670103/169, 250519128231756643/2197)
(38497791473737/546121, 175891707053486554291/403583419)

Commentary

BASE records/family_Z4.md#28 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:21:26 UTC · history

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