curve #290

y² + xy + y = x³ − x² − 143064121313070058971349202x + 644033892656805018000831946914423333329

a-invariants: [1, -1, 1, -143064121313070058971349202, 644033892656805018000831946914423333329]
c-invariants: [6867077823027362830624761681, -556445283255448633702515179001323948568921]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 573016129202728438463406209148046191362181279694355936916964827270
discriminant (Δ): 8216303602985225953011427955932287320725712053093517989543396386002303631360000
Faltings height: 13.9250
naive height: 192.2896
primes of bad reduction: 2, 3, 5, 7, 4011551, 226732605775896226490763286077790048834961474800492471879
regulator: 3440505841756924919.941279609431056829450887349567148455765747076880575881181
submitted by: 7fff-zip
submitted at: 2026-08-23 15:35:24 UTC
last updated: 2026-08-23 15:35:24 UTC

(-3068672516463, -32467734832606078769)
(6715307774263977177/2524921, -67416626864103197872394848861/4012099469)
(95012073250968801/10609, 9840134593745201491613449/1092727)
(-2921704246035672527/762129, 22426402698405485594593846327/665338617)
(15284970673019329/1521, 882241190350018844319337/59319)
(852546242503545297/7612081, 526307011895579077065261425849/21001731479)
(24101727065013081/1849, -2506663797462602334395651/79507)
(1537142394063682303/190969, -312091292961137276489942157/83453453)
(35860763833611/4, -72447888147260864491/8)
(1365874652451236880297/30349081, -48848891281661520816383064097901/167193087229)
(4295405444791857/529, 51235650422122792594121/12167)
(2909415607596667, -156929642734920700769699)
(14035352401270878513/2879809, -38649750848808156301185398737/4887035873)
(236715644710497, 3637440345541084338031)
(1744151361277016953/24649, -2272412977540368477032136197/3869893)
(5889811060617, 2393750193677952031)
(897421117167433/169, 12824516270521547666907/2197)
(28867361197230961730833/663217009, -4735736960912795829598381013543513/17079827632777)
(23774226340603/4, -15358084415602060287/8)

No commentary yet.