curve #2793

y² + xy = x³ − 349960450236374537044731366104096847315x + 2334228106621384646411703013971250553516398106559474797217

a-invariants: [1, 0, 0, -349960450236374537044731366104096847315, 2334228106621384646411703013971250553516398106559474797217]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/10ℤ
conductor (N): 37185313994818665091723230
discriminant (Δ): 389265685852499587475689943803192579535767574333652197305066818077610977982035697425443337607158400406783110000000000
Faltings height: 21.1141
naive height: 277.8663
primes of bad reduction: 2, 3, 5, 7, 11, 29, 83, 181, 2099, 2733361, 6440141
regulator: 14916789.41056441442294480058774452804749073516
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:22:41 UTC
last updated: 2026-09-26 20:22:41 UTC

(27871728089570766822518550306/1952137489, 1358573678733666234270912721506451253111211/86251290676487)
(79683221958290183275583671483164/9703418130961, 113757749527935178347203593091878214202979830333/30226448283905574791)
(33026790339998050436047234709581888880376212714/9804544701240252493986308161, 33540608912457629088874029577586902533526527356898735736949738801518267/970825435725653250476084979911365621664159)
(736337187123421188570624534418924717252369265410496142/9168290659335385099399214430138049, 615933984744210480360486565011634252817560601953373667789965845887943908189546873/877874753963421185196947919583452248308798801730593)

Dujella (2008). Source: https://dujella.github.io/tors/z10.html (curve entry 5). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:22:41 UTC · history