curve #6228

y² + y = x³ − 2088209695103894294

a-invariants: [0, 0, 1, 0, -2088209695103894294]
c-invariants: [0, 1804213176569764669800]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 2215564848694462660775701182225
discriminant (Δ): -1883787723673588440549496729486286476875
Faltings height: 6.2151
naive height: 97.8888
primes of bad reduction: 3, 5, 7, 13, 37, 593, 5737, 8663
regulator: 83680840112283.6291100961018999415264512664614661594869184798
submitted by: jesper-petersen
submitted at: 2026-10-31 08:48:41 UTC
last updated: 2026-10-31 08:48:41 UTC

Witness: 11 independent points log in to add more points →

(7815483166/5041, 458130271671671/357911)
(663070907776/356409, 443831932874004677/212776173)
(455836957234/100489, 304299443301697958/31855013)
(3362053063828174/2934369, -194942640928026112811279/5026574097)
(38992159581064/45369, -243481480127650602674/9663597)
(482593294114/13225, -335245218351621638/1520875)
(14052749656/8281, -1260675903590069/753571)
(9127612443226/5631129, 19687024614441281005/13362669117)
(19401465637324/11909401, 61446944956556717419/41099342851)
(1087825312246/332929, 1100106002999100865/192100033)
(3397946495736601/2649778576, 19538897028219324932963/136400001978176)

Commentary

Bruin–Nasserden rational parametrization of the Burkhardt quartic with parameters (u,v,w)=(5/4,1/4,15/8), specialized at t=-51/572. PARI/GP 2.17.4 returned rank bounds [11,11] for the source curve and its isogenous partner has eleven independent rational points.

last edited by jesper-petersen at 2026-10-31 08:48:41 UTC · history