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curve #4245

y² = x³ + x² − 40806227465x + 3168820981473079

a-invariants: [0, 1, 0, -40806227465, 3168820981473079]
c-invariants: [1958698918336, -2737873080186250240]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 24713621597826872896
discriminant (Δ): 10765186557324986785105664970752
Faltings height: 4.8571
naive height: 84.9099
primes of bad reduction: 2, 23, 73, 79, 97, 593, 809, 857
regulator: 227301.76240993300988568596089655567662481503836362355729
submitted by: Michael Rubinstein
submitted at: 2026-10-15 18:11:39 UTC
last updated: 2026-10-15 18:11:39 UTC

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

(126679, -5695168)
(124425, -4221052)
(79805, 20507352)
(-227590, 25834773)
(42729, -38771468)
(1696171/25, 3336737144/125)
(200279, 55043232)
(282826, 119378579)
(89741, -15151296)

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 18:11:39 UTC · history

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