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curve #783

y² = x³ − 83202007x + 213124102810

a-invariants: [0, 0, 0, -83202007, 213124102810]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 48977152040385241435576
discriminant (Δ): 17239957518215604985322752
Faltings height: 3.5504
naive height: 66.3239
primes of bad reduction: 2, 11, 457, 1217852398060106461
regulator: 4336471.37710966009153666868407522805296270363027432836893684
submitted by: Michael Rubinstein
submitted at: 2026-09-18 12:39:23 UTC
last updated: 2026-09-18 12:39:23 UTC

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

(281, 435622)
(-9707, 325754)
(2349, 175054)
(7431, 72028)
(2833, 12254)
(12837, 1122698)
(-9102, 465146)
(-4757, -708004)
(10401, 687698)
(8487, -343948)
(-10147, -112354)

Commentary

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

last edited by Michael Rubinstein at 2026-09-18 12:39:23 UTC · history

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