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curve #1723

y² + xy + y = x³ + x² − 520933723916648280x + 149299702648946892139084825

a-invariants: [1, 1, 1, -520933723916648280, 149299702648946892139084825]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/5ℤ
conductor (N): 1250201285870129810
discriminant (Δ): -581978296702355419780532789088264694519235995750400000
Faltings height: 9.0872
naive height: 134.0591
primes of bad reduction: 2, 5, 7, 43, 139, 349, 8561960471
regulator: 69941.747072182557268090402948270784189671853336199
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:16:07 UTC
last updated: 2026-09-25 06:16:07 UTC

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

(846448493, 17742613872853)
(11508938333, 1232300192295653)
(32796677173/81, 1589448199374037/729)
(-39809359019/49, 2065983360817755/343)
(354577255, -3027996451175)
(3227615521/9, 79190478803875/27)

Commentary

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:16:07 UTC · history

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