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curve #4242

y² = x³ + x² − 17465296335x + 5229643552629409

a-invariants: [0, 1, 0, -17465296335, 5229643552629409]
c-invariants: [838334224096, -4518417059477153920]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 7623567598977423232
discriminant (Δ): -11473905005735170697065393673644288
Faltings height: 5.2164
naive height: 85.9094
primes of bad reduction: 2, 17, 47, 89, 257, 769, 2801
regulator: 400018.05740465824960085853111125030275048877361551766655
submitted by: Michael Rubinstein
submitted at: 2026-10-15 18:11:07 UTC
last updated: 2026-10-15 18:11:07 UTC

Witness: 9 independent points log in to add more points →

(956720, -929634103)
(-181056, -49564367)
(-577819/4, -550679401/8)
(291801, 158049226)
(37934440, -233640381603)
(53145, 66719978)
(22809961/81, 109696824154/729)
(1947192, -2711846971)
(929481/16, 4250626739/64)

Commentary

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

last edited by Michael Rubinstein at 2026-10-15 18:11:07 UTC · history

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