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curve #4362

y² + y = x³ + x² − 338633773513013170x + 75847892516845450142793256

a-invariants: [0, 1, 1, -338633773513013170, 75847892516845450142793256]
c-invariants: [16254421128624632176, -65532579232080995695121166424]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 2923539936092655
discriminant (Δ): -2481299863378019147500476673396758310546875
Faltings height: 8.3609
naive height: 132.7047
primes of bad reduction: 3, 5, 11, 17, 19, 149, 4751, 77491
regulator: 12434.3358070392625328051376510880939109833108526
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:06:21 UTC
last updated: 2026-10-17 10:06:21 UTC

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

(335998685, 812282812)
(335973185, 6712312)
(2661824416385/7921, 1643085964300328/704969)
(4290013240640/12769, 98268821093864/1442897)
(1991982712505/5929, 5221626518051/456533)

Commentary

BASE torsion/torsion_Z5.tsv.gz:1323 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:06:21 UTC · history

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