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curve #4325

y² + xy + y = x³ − 848045096418335x + 9505533937802574570582

a-invariants: [1, 0, 1, -848045096418335, 9505533937802574570582]
c-invariants: [40706164628080057, -8212781383320671371103149]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 1387579280932932129238
discriminant (Δ): 2618311886049646541221533473080034200364
Faltings height: 7.0539
naive height: 114.7355
primes of bad reduction: 2, 7, 37, 43, 73, 97, 433, 2029, 232877
regulator: 6169187.03282611110039874931959743331405300371091743941
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:04:53 UTC
last updated: 2026-10-17 10:04:53 UTC

Witness: 8 independent points log in to add more points →

(3907430469/289, 111041282554908/4913)
(225649579/4, 3005792118523/8)
(294556469/16, 736531098959/64)
(13407081, 23352343796)
(2847004684/169, 495716022017/2197)
(34795152955/2116, 253554299964473/97336)
(305769995897/19321, 18625736551838908/2685619)
(377274631341/21025, -24787249714712874/3048625)

Commentary

BASE torsion/torsion_Z3.tsv.gz:7105 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:04:53 UTC · history

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