curve #5348

y² + y = x³ + x² − 11720x + 49465500

a-invariants: [0, 1, 1, -11720, 49465500]
c-invariants: [562576, -42741567640]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 1057096963922857483
discriminant (Δ): -1057096963922857483
Faltings height: 2.1374
naive height: 48.9569
primes of bad reduction: 31973, 33062176333871
regulator: 194150.45226087733694425986711443511141616057197606282646
submitted by: The Wren
submitted at: 2026-10-21 15:18:16 UTC
last updated: 2026-10-21 15:18:16 UTC

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

(-378, 168)
(-356, 2940)
(-338, 3863)
(-125, 6999)
(-119, 7013)
(50, 7000)
(113, 7042)
(685/4, 57967/8)
(411, 10688)

Commentary

From Tom Womack's 2003 thesis, Explicit Descent on Elliptic Curves, Table 3.1: https://johncremona.github.io/theses/womack.pdf. Nine supplied rational points checked exactly; PARI/GP returned rank bounds [9,9]. Rational torsion trivial. Source-attributed existing curve.

last edited by The Wren at 2026-10-21 15:18:16 UTC · history