curve #6438

y² + xy + y = x³ − x² − 5417336169275030014965138x + 5729006841382451704031809736436342417

a-invariants: [1, -1, 1, -5417336169275030014965138, 5729006841382451704031809736436342417]
c-invariants: [260032136125201440718326609, -4949861910953268127670920205797767378777]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 1655427940556757048778214729243609440808856889356705562140415015630
discriminant (Δ): -4003828082032451183257846715694147594685701390448015361362625570526013030400
Faltings height: 13.2266
naive height: 182.8004
primes of bad reduction: 2, 5, 11, 61, 4127, 178817, 6831372802873, 4448809566470151911033980808252632126489
regulator: 52337129738140288418.4956941188915161258631302284854766243702587722943636920500
submitted by: apkorte
submitted at: 2026-11-03 04:44:34 UTC
last updated: 2026-11-03 04:44:34 UTC

(1453550200381, 962137271494097659)
(1293313564065, 941257195959629423)
(1342037252823, -935861161537995607)
(5998221537881, 13749273613536393959)
(8800047814225/9, 31566280422794118637/27)
(16655871643273/9, -38580054311682832651/27)
(23039025418097, 110045239831640356687)
(20226745466953, 90395481785097838303)
(5698396744593, -12644988048702209697)
(1780085890657, 1313868056532616815)
(2067557093473, -1834866759586733457)
(-2702637973945, -793318517591350247)
(-2634091690513, 1312358899761632897)
(1604350994385, -1080373312036193649)
(14962770198753, -57224153222681289297)
(2788403736353, 3507657414961451503)
(-2736976323183, -230931987515395233)
(-2521748145969, 1831347458358998369)
(80911183582881, -727504094435527428241)
(35512336711087/9, -182699302480511697869/27)

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