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curve #3456

y² + y = x³ − 445365697x + 5911837823466

a-invariants: [0, 0, 1, -445365697, 5911837823466]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 27639151875789191304731
discriminant (Δ): -9444657504931551928313544203
Faltings height: 4.0640
naive height: 72.3391
primes of bad reduction: 31, 73, 151, 29333, 2757444175039
regulator: 3172305.91288850279903802275433741832941522079390016606382748
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:38:02 UTC
last updated: 2026-09-27 05:38:02 UTC

Witness: 11 independent points log in to add more points →

(-2820, 2673077)
(653, 2370926)
(19226, 2110904)
(-21946, 2261868)
(11999, 1515078)
(7473, 1732326)
(-25923, 191694)
(206617, 93458505)
(-2233071/100, 2172952467/1000)
(1064869/25, 1001731597/125)
(30103, 4447926)

Commentary

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

last edited by Michael Rubinstein at 2026-09-27 05:38:02 UTC · history

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