curve #3815

y² = x³ + x² − 6214354189123088303142197175909321x + 197691119063941253591168663874268504563225597543579

a-invariants: [0, 1, 0, -6214354189123088303142197175909321, 197691119063941253591168663874268504563225597543579]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 4330734016329627881037849639640772795649802644695975357744191889843583500955240
discriminant (Δ): -1524150068209296856607211561378287705413082621092311468556789733489200630238832369237219763212285561600
Faltings height: 18.3637
naive height: 245.1447
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 29, 3463, 644197, 14170917208705331, 44811231436207394238233639572163578842073
regulator: 15005531498554564718781.3017666548832345032504932131654472383964700519527196578667966
submitted by: 7fff-zip
submitted at: 2026-10-03 04:56:10 UTC
last updated: 2026-10-03 04:56:10 UTC

(46196701631490054, 3032896594907348082666225)
(371134715117039475, -221386058095514761097914902)
(3446289876653764365981/49729, 110818289472946879512346581348810/11089567)
(54668396771805054, -4620188992768098193919475)
(8318098516787181381/4, -23973342883515709019728203735/8)
(-83234174015803587/4, 142658814960412149563113131/8)
(46510917055440999, 3044875146387924865168230)
(-146551131852953019/4, 155165230881423679446972585/8)
(241566325950610176502/4761, 1184691677888420285241967696387/328509)
(-69655866791263675, -17105299639843271805898002)
(-87774636970888949361/961, -54296182872822281778364322730/29791)
(37057476235824433711/1089, -181927071427858889583797087210/35937)
(1654898510269931934, -2126538512006018380659236925)
(11695138229874099, 11252244445405060334599530)
(119738517824337095901/2209, -465537305170735745619979116810/103823)
(53983389652840299981/1444, 230324938524109547371524386115/54872)
(266847288266100087, 132442173160348861815846918)
(-693825511130619035/9, -399198414297564123605152174/27)
(47004760637836239, 3072692602279320576626070)
(-65532378420065804721/2401, -2191469125983019046913520020150/117649)
(36481839143273427981/169, -207445653388846193434129764090/2197)
(-64503042453308130, 18170354213788745064003453)
(104724277789193400051/1849, 416260028070793890352339225710/79507)

X1008 at T=-111/11.

last edited by 7fff-zip at 2026-10-03 04:56:10 UTC · history