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curve #3799

y² + xy + y = x³ + x² − 1043438552121560x + 12973238863652488323737

a-invariants: [1, 1, 1, -1043438552121560, 12973238863652488323737]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 13531221841830
discriminant (Δ): 867487453425269964881026933566195360000
Faltings height: 7.0710
naive height: 115.3575
primes of bad reduction: 2, 3, 5, 7, 11, 17, 89, 97, 167, 239
regulator: 1167.55033331774701603927086054450254048478333292
submitted by: Daniel Błażewicz
submitted at: 2026-10-02 05:31:18 UTC
last updated: 2026-10-02 05:31:18 UTC

Witness: 5 independent points log in to add more points →

(17743967, 6711174041)
(20532717, 14309290741)
(28606797, 80819749021)
(100018393/9, 1415701770527/27)
(69390085707/3721, -522166005779/226981)

Commentary

(u,v) = (14960,97) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5.

last edited by Daniel Błażewicz at 2026-10-02 05:31:19 UTC · history

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