curve #5745

y² = x³ + 97403770623166588

a-invariants: [0, 0, 0, 0, 97403770623166588]
c-invariants: [0, -84156857818415932032]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 35563286457515224348725967345296
discriminant (Δ): -4098597637655714575741970284610673408
Faltings height: 5.7042
naive height: 91.7584
primes of bad reduction: 2, 3, 7, 1861, 38148308389
regulator: 97991077624407290.5075551282190292743916509957336792922151840
submitted by: jesper-petersen
submitted at: 2026-10-24 18:14:07 UTC
last updated: 2026-10-24 18:14:07 UTC

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

(-1932418664437723/4558005169, 44804865009416676171525/307724602974697)
(-35790900957905702/105944391081, 8365358882639383595646830/34483945797345771)
(93586051822834109/119373705025, 31390307539685513685760977/41244211954662625)
(191904558821452757/190858018129, 88002969830411413558926285/83380714954070617)
(-25621481423068327958/79079348519649, 177057122358608871655755283210/703225522168696317393)
(-1984841713426939888486/6884899580337025, 154818988550823527481302450113338/571276573723840848797375)
(11514965055216223889609986/9612400324865765625, 40166293238107476255391931870402079766/29802162207559637097017578125)
(1818473317109196375304745098/8283720430150625408481, 247750977920305863915937785987290877213590/753942369211446545577895610045871)
(4207117521377477446924873738/38823763945993574761161, 2402994855905119545869819907513897942882050/7649736160940116778631420164350341)
(440211583891544154014664917919698/108685163885786325719588281, 9242943138016935655366067654921110311958588866150/1133066493192539092365560282238373423571)
(12629249026976452437711652417783751066/62223326691793588384014330625, 44881389385442869387657637983386963878169172872806572614/15521362416458035097888900946091007734890625)

Commentary

The rationally 3-isogenous partner of the Burkhardt-quartic Mordell curve constructed using parameters (u,v,w)=(9/6,-9/6,-1/6) and specialization t=-1133/838. PARI/GP 2.17.4 returned matching computational rank bounds [11,11] for this model and its original 3-isogenous curve.

last edited by jesper-petersen at 2026-10-24 18:14:07 UTC · history