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curve #279

y² = x³ − 2010516977329x + 71337059553120256

a-invariants: [0, 0, 0, -2010516977329, 71337059553120256]
c-invariants: [96504814911792, -61635219453895901184]
rank (lower bound): ≥ 7
torsion subgroup: trivial
conductor (N): 385416359790793559534096847392
discriminant (Δ): 517921148392114641290176902572660474944
Faltings height: 6.1181
naive height: 96.6018
primes of bad reduction: 2, 7, 23, 464652646250619140289361
regulator: 1061855.610465193810272031194090256742618647434667954
submitted by: Daksh Shami
submitted at: 2026-08-21 20:24:14 UTC
last updated: 2026-09-02 14:44:30 UTC

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

(-1100113, 975562756)
(-588455, 1025020024)
(-11431, 307112008)
(0, 267089984)
(1417927, 267089984)
(2514337, 3303268556)
(37547776/25, 82881256976/125)

Commentary

Found during a preliminary search among rational specializations of the classical one-parameter family y^2 = x^3 - u^2*x + 1, at u = 8807/2576.

last edited by Daksh Shami at 2026-08-21 20:24:14 UTC · history

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