curve #5347

y² + y = x³ + x² + 44518x + 49327152

a-invariants: [0, 1, 1, 44518, 49327152]
c-invariants: [-2136848, -42605838424]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 1056142691473638331
discriminant (Δ): -1056142691473638331
Faltings height: 2.1378
naive height: 48.9505
primes of bad reduction: 1056142691473638331
regulator: 235638.56167515540553625080987190810683820215506851138791
submitted by: The Wren
submitted at: 2026-10-21 15:17:08 UTC
last updated: 2026-10-21 15:17:08 UTC

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

(-315, 2036)
(-302, 2903)
(-294, 3303)
(-219, 5396)
(-37, 6901)
(172, 7880)
(255, 8793)
(507, 14229)
(783, 23766)

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 15:17:08 UTC · history