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curve #1343

y² + xy = x³ − 3710928957486x + 2742767919738736516

a-invariants: [1, 0, 0, -3710928957486, 2742767919738736516]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 49042759535775430
discriminant (Δ): 20763576372831659492584658815537049600
Faltings height: 6.0209
naive height: 98.4405
primes of bad reduction: 2, 5, 17, 19, 29, 37, 41, 59, 811, 7213
regulator: 3105.509447844835170463160519459544114167783322988178
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:35:35 UTC
last updated: 2026-09-24 17:35:35 UTC

Witness: 7 independent points log in to add more points →

(14931796, -57248214518)
(1164244, -21376862)
(1058300, -28581054)
(867730, -420011834)
(1607944, -966783242)
(975396, 225636322)
(949976, -273942938)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:35:36 UTC · history

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