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curve #3797

y² + xy + y = x³ + x² − 565445572543774x + 3709875070735373782826

a-invariants: [1, 1, 1, -565445572543774, 3709875070735373782826]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 18837563596761
discriminant (Δ): 5624815709957510255480734201095247126829130609
Faltings height: 7.4856
naive height: 113.5195
primes of bad reduction: 3, 7, 13, 19, 23, 29, 31, 37, 47, 101
regulator: 5220.39959026273334076127896009804619435662994367
submitted by: Daniel Błażewicz
submitted at: 2026-10-02 05:29:59 UTC
last updated: 2026-10-02 05:29:59 UTC

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

(-26550964, 2421794829)
(47443486, 289239081919)
(-212817286/25, 11115315882903/125)
(-41553403/16, 4597791529263/64)
(19961250874/2809, 1058119652275143/148877)

Commentary

(u,v) = (13547,6956) 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 05:30:00 UTC · history

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