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curve #4381

y² + y = x³ + x² − 77498250893530x + 283723382284692707434

a-invariants: [0, 1, 1, -77498250893530, 283723382284692707434]
c-invariants: [3719916042889456, -245137024613470756559896]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 967393423544955
discriminant (Δ): -4986573063609402571963670085770774848096875
Faltings height: 6.9341
naive height: 107.7122
primes of bad reduction: 3, 5, 11, 89, 577, 4219, 27061
regulator: 10243.9108903223871531584537921091283450145482983
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:09:23 UTC
last updated: 2026-10-17 10:09:23 UTC

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

(7158581, 9787207402)
(-8028522391/1024, 663000858238901/32768)
(338327365814/80089, 127665042084590194/22665187)
(1559589629/4, 61575198513671/8)
(66536309/4, 479809069901/8)

Commentary

Curve from torsion/torsion_Z5.tsv.gz:1302 (mrubinst/elliptic-curves-by-rank) + Werr 4-Pillar Algebraic Sieve factorization.

last edited by Volkan Dagli at 2026-10-17 10:09:23 UTC · history

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