curve #4575

y² + xy = x³ − 2191024393477x + 1248299611172253249

a-invariants: [1, 0, 0, -2191024393477, 1248299611172253249]
c-invariants: [105169170886897, -1078531021806583137481]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 120716374135263686
discriminant (Δ): 105234351003688265562972962645504
Faltings height: 5.5822
naive height: 96.8598
primes of bad reduction: 2, 13, 19, 31, 37, 241, 1123, 3187
regulator: 23605.77209750634050597740672639365125900560224601426
submitted by: The Wren
submitted at: 2026-10-18 02:10:47 UTC
last updated: 2026-10-18 02:10:47 UTC

Witness: 7 independent points log in to add more points →

(784500, 110305557)
(836642, 28233367)
(854374, -244225)
(866278, 18305307)
(852142, -4347633)
(440834, 606484551)
(157418, -952598433)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z3.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Seven supplied rational points checked exactly and certified independent modulo torsion. Rational torsion C3. Source-attributed existing curve.

last edited by The Wren at 2026-10-18 02:10:47 UTC · history