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curve #4365

y² + xy = x³ − 264708966101580x + 5513726414288008940400

a-invariants: [1, 0, 0, -264708966101580, 5513726414288008940400]
c-invariants: [12706030372875841, -4763859641003885283819361]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 170538660294990
discriminant (Δ): -11946213181088721157470353312926212514687500000
Faltings height: 7.5252
naive height: 113.6462
primes of bad reduction: 2, 3, 5, 13, 31, 41, 15331, 22441
regulator: 2604.35649299856245318072402063069238593322534422
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:06:25 UTC
last updated: 2026-10-17 10:06:25 UTC

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

(1078360140, 35407123447020)
(42452670, 266034342210)
(834480660, 24101073987120)
(598826085/16, 14025174982455/64)
(10232820, 62256364560)

Commentary

BASE torsion/torsion_Z5.tsv.gz:1290 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:06:26 UTC · history

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