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curve #4335

y² + xy + y = x³ − 653466460x + 6429170239500

a-invariants: [1, 0, 1, -653466460, 6429170239500]
c-invariants: [31366390057, -5554850136513301]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 21820427847974
discriminant (Δ): 2011664174461092729139814
Faltings height: 3.7202
naive height: 72.5070
primes of bad reduction: 2, 7, 19, 43, 61, 103, 113, 2687
regulator: 20369.774469792387005424036504668239579169622460413
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:19 UTC
last updated: 2026-10-17 10:05:19 UTC

Witness: 6 independent points log in to add more points →

(3659249/256, -420049137/4096)
(59547/4, -212553/8)
(139796/25, 214343091/125)
(4517012/841, 42697729356/24389)
(10677658/729, -414845261/19683)
(241426/9, -77692669/27)

Commentary

BASE torsion/torsion_Z3.tsv.gz:487 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:19 UTC · history

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