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curve #4244

y² = x³ + x² − 120297676508x + 12354729763545988

a-invariants: [0, 1, 0, -120297676508, 12354729763545988]
c-invariants: [5774288472400, -10674521161434568000]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 16935100540754779100
discriminant (Δ): 45476433130431311139458887100000000
Faltings height: 5.3618
naive height: 88.1533
primes of bad reduction: 2, 5, 29, 71, 109, 281, 509, 1669
regulator: 421833.80130824456805185716017571289609635589187761224742
submitted by: Michael Rubinstein
submitted at: 2026-10-15 18:11:28 UTC
last updated: 2026-10-15 18:11:28 UTC

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

(274388, 2214150)
(5268, 108264250)
(3426412/9, 3980761750/27)
(1807033/16, 925145675/64)
(277768, 19265750)
(4885852, 10772997778)
(8645308/81, -19709625250/729)
(-348132, 109736750)
(-49232, -134751250)

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 18:11:28 UTC · history

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