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curve #6044

y2 + xy + y = x3 − 353824411x + 2561679557130
a-invariants
[1, 0, 1, -353824411, 2561679557130]
c-invariants
[16983571705, -2213316612718093]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/3ℤ
conductor (N)
23522954
discriminant (Δ)
-47045908
Faltings height
2.9848
naive height
70.6665
primes of bad reduction
2, 7, 13, 307, 421
regulator
497.42458280692211117731494668010236905376372
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained in my own bounded discriminant-first search of the integral Tate X_1(3) family, following the method described by jesper-petersen on curve #3759. The specialization a=361, b=-1 in y^2+a*x*y+b*y=x^3 gives y^2+361*x*y-y=x^3, with discriminant -47045908. The displayed equation is its global minimal model. All three listed rational points were checked exactly and returned as an independent set, with rank bounds [3,3]. The rational torsion subgroup is Z/3Z.

last edited by The Wren at · history

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