curve #5726

y² = x³ + 18878192524572

a-invariants: [0, 0, 0, 0, 18878192524572]
c-invariants: [0, -16310758341230208]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 9622426130859765856242145968
discriminant (Δ): -153958818093756253699874335488
Faltings height: 4.2794
naive height: 74.6612
primes of bad reduction: 2, 3, 89, 457, 863, 44819
regulator: 20481589501008.81725186433054199118071077980398257235186850
submitted by: jesper-petersen
submitted at: 2026-10-24 16:57:58 UTC
last updated: 2026-10-24 16:57:58 UTC

Witness: 10 independent points log in to add more points →

(-4701197906774/178623225, 1920458221910770474/2387299402125)
(-11393585412971/1195430625, 175417329581274933917/41332013859375)
(-9355198422782/35733475089, 29348971009120685624950/6754805996498937)
(1225334502226/502880625, 49016680942590231974/11277098015625)
(2167334127226/544055625, 55229502000467018026/12690097453125)
(4775165262291058/172020051009, 452745611729022242996810/71345832216135777)
(76387317093082/2486917161, 857954987358466776490/124020071901909)
(17958098736106306/396125478225, 2639090923587344805745546/249315434112641625)
(9786390274170226/59978459025, 970231677574383529807526/14689024507517625)
(-708545521976207/77697102564, 92190048837032322822025/21657445762894488)

Commentary

The rationally 3-isogenous partner of a Mordell curve constructed using the Bruin–Nasserden parametrization of the Burkhardt quartic with parameters (u,v,w)=(9/5,-8/5,18/5) and specialization t=80/43. The specialization was selected using a three-stage Mestre–Nagao sieve. PARI/GP 2.17.4 returned matching computational rank bounds [10,10].

last edited by jesper-petersen at 2026-10-24 16:57:58 UTC · history