curve #33

y² = x³ + x² − 1033620669162578745x + 404204621142300751511020144

a-invariants: [0, 1, 0, -1033620669162578745, 404204621142300751511020144]
c-invariants: [49613792119803779776, -349232792964630602024344083040]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ
conductor (N): 535701165729047061464726179383779596
discriminant (Δ): 93873316108015714157059941602262270600638822314912592
Faltings height: 9.0964
naive height: 136.0524
primes of bad reduction: 2, 13, 17, 23, 29, 31, 37, 41, 43, 47, 53, 59, 3057053387069549573
regulator: 16764246962.6599538425546112945285195822333923272100049593443
submitted by: David Renshaw
submitted at: 2026-05-27 22:12:12 UTC
last updated: 2026-07-01 22:49:32 UTC

(567020697, 651563123419)
(572060549, 345977302867)
(618262355, 1218864665837)
(9588741225/16, 1394897103107/64)
(2062532261/4, 23090550241369/8)
(573619772, 207397662806)
(553608987, 1286321677901)
(647275079, 2520583821587)
(573703341, 197837573149)
(611109417, 878062026491)
(23257761261641/38809, 77388276951103391/7645373)

Found by Schneiders - Zimmer (1991). A curve of rank exactly 11, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:32:05 UTC · history