curve #4971

y² + y = x³ + x² − 87382462760x + 9942412342455314

a-invariants: [0, 1, 1, -87382462760, 9942412342455314]
c-invariants: [4194358212496, -8590269430030666456]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/5ℤ
conductor (N): 46327034985
discriminant (Δ): -1673263746076914230037847846875
Faltings height: 4.9132
naive height: 87.1943
primes of bad reduction: 3, 5, 7, 11, 17, 29, 81359
regulator: 56.04096760361484204165027194443792586182099887
submitted by: The Wren
submitted at: 2026-10-21 00:34:22 UTC
last updated: 2026-10-21 00:34:22 UTC

Witness: 4 independent points log in to add more points →

(1091269/4, 640431221/8)
(1219789/4, 863606201/8)
(2723233/16, 35378311/64)
(10936129/64, 238663169/512)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, families/family_Z5.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Four supplied rational points checked exactly; PARI/GP returned rank bounds [4,4]. Rational torsion C5. Source-attributed existing curve.

last edited by The Wren at 2026-10-21 00:34:22 UTC · history