curve #5741

y² + y = x³ + 11842496149371824

a-invariants: [0, 0, 1, 0, 11842496149371824]
c-invariants: [0, -10231916673057256152]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 83107979287636435376946891717267
discriminant (Δ): -60585716900686961389794284061887643
Faltings height: 5.3530
naive height: 87.5441
primes of bad reduction: 3, 23, 4423, 5748750353
regulator: 2841328150044107.62525104336400091734477319628037498592625991
submitted by: jesper-petersen
submitted at: 2026-10-24 18:11:13 UTC
last updated: 2026-10-24 18:11:13 UTC

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

(-1174204090960868/6956727649, 48663849783881113391361/580239783020143)
(-935810222002688/8751041209, 84361439603518949269661/818633651978323)
(673000769698864/18062016025, 264738705381451462479888/2427444643679875)
(760179897815614/18491920225, 274450961782967198939112/2514623771796625)
(1631976483295798/22550728561, 374372012077708760288303/3386420357276809)
(8756930678610364/47985093025, 1407117802226327944528737/10511374552591375)
(82987173744904042/192929142169, 25623516584917418730816011/84741617618885053)
(465369771913952356/13041668255625, 5135146882124194148500782379/47097702613244953125)
(-264457463115765652463/2155515356190784, 10005383359654217802232176102009/100075249553977597501952)
(-18397013150462122586/108298260156025, 93891437581171509907655369163/1127021547561396786125)
(56878029525999260986/2012867776350025, 9836889986000266182872775331016/90307302721604989874875)

Commentary

The rationally 3-isogenous partner of a Mordell specialization constructed from the Burkhardt quartic with Bruin–Nasserden parameters (u,v,w)=(9/6,-12/6,-10/6) and t=-421/568. PARI/GP 2.17.4 returned matching computational rank bounds [11,11] for both isogenous models.

last edited by jesper-petersen at 2026-10-24 18:11:14 UTC · history