curve #3153

y² + xy = x³ − 83598958924587909464854346830766301770x + 294558475635028689022196236625520239031964650641823108900

a-invariants: [1, 0, 0, -83598958924587909464854346830766301770, 294558475635028689022196236625520239031964650641823108900]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/4ℤ
conductor (N): 14957195101499347727901912655348880567251830
discriminant (Δ): -90013882772824882914010972855353684388195792055576885220030341532698166103991650012539993500264351819366400000000
Faltings height: 20.5779
naive height: 273.5733
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 29, 43, 71, 103, 151, 797, 94253, 253424587069203922319
regulator: 14989041581.2229782767808353582314131997414733219354277488587
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:39:49 UTC
last updated: 2026-09-26 20:39:49 UTC

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

(-376658071791198860, -18055283474071165325696694170)
(5126975891755967860, 845996987662141966273374310)
(3061243374503166190, 8205441734919964615103472280)
(1941917047927221472, 11812674654292737888137594566)
(620417310829718740, 15586245343508460341818496230)
(5301357312000892480, 601609041349147923620788090)
(2881859166491031610, 8807508921706068412899766810)
(4170532698807427752, 4294856170447441908261060786)
(-3328999758526185560, -23150952839357719761727450970)
(5122395271209196780, 858924728430079776471759430)
(860309498550198580, 14942363941257491522837379430)

Commentary

Khoshnam - Moody (2016). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 6). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:39:50 UTC · history