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curve #4047

y² + xy = x³ − 909720834x + 10534658919939

a-invariants: [1, 0, 0, -909720834, 10534658919939]
c-invariants: [43666600033, -9102010806727345]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 17406567453
discriminant (Δ): 240536885211427087493988129
Faltings height: 3.9330
naive height: 73.4995
primes of bad reduction: 3, 11, 37, 47, 53, 59, 97
regulator: 83.7913534011294423846532976197665397994410240158
submitted by: Michael Rubinstein
submitted at: 2026-10-07 22:24:04 UTC
last updated: 2026-10-07 22:24:04 UTC

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

(11451, -1278123)
(8154795, 23283087168)
(18282, -125961)
(-465/4, 26096181/8)
(148170/49, 958129689/343)

Commentary

Torsion Z/2+Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-10-07 22:24:04 UTC · history

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