curve #5734

y² = x³ − 2585480502296488

a-invariants: [0, 0, 0, 0, -2585480502296488]
c-invariants: [0, 2233855153984165632]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 180487154549393097036530142621888
discriminant (Δ): -2887794472790289552584482281950208
Faltings height: 5.0994
naive height: 84.5005
primes of bad reduction: 2, 3, 733, 440907316217
regulator: 21666945699510707.2905259985173071808689602052261187976635126
submitted by: jesper-petersen
submitted at: 2026-10-24 17:24:55 UTC
last updated: 2026-10-24 17:24:55 UTC

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

(212530266880521553/1480244522409, 34843347512815166957344195/1800943938922477077)
(59893448435640718/261659871729, 12982025360933556977217140/133846089205920183)
(769567516296746/2675475625, 20155602706021088346544/138388976703125)
(71297348564494618/73942117929, -19010034694881004540036040/20106562533607467)
(128629239372098926/857522300625, -22313563056218252794443076/794087088436265625)
(103911191177718935246/28962318172225, 1059208185194010021002192469956/155865494026327254625)
(881694641798478137297/1045106308234816, 26124035196746059877209820037095/33786305423671188068864)
(74039395067822458721/385389313882225, -507817717433423376035879609269/7565706726242109520375)
(158727655609392112181209/420117167207091600, 61703691197272645049100429292995427/272305016819514235084536000)
(19227448884236373969242234/9231878783376483025, -84298596697215265129433367274769519648/28050146911566860469815702375)
(7386431016920068742826014/8396034327678765625, 20036684283983311060508699465000779412/24328274553077333125955078125)

Commentary

Constructed through the Bruin–Nasserden parametrization of the Burkhardt quartic with parameters (u,v,w)=(-18/5,1/5,-10/5) and specialization t=-1831/1135. PARI/GP 2.17.4 returned rank bounds [11,11].

last edited by jesper-petersen at 2026-10-24 17:24:55 UTC · history