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curve #6035

y2 + xy = x3 − x2 − 974026287x + 11700735677865
a-invariants
[1, -1, 0, -974026287, 11700735677865]
c-invariants
[46753261785, -10109225235997341]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/3ℤ
conductor (N)
5585814
discriminant (Δ)
-100544652
Faltings height
3.2169
naive height
73.7044
primes of bad reduction
2, 3, 13, 73, 109
regulator
622.58784182109980938511716570188108780513994
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=465, b=-1 in y^2+a*x*y+b*y=x^3 gives y^2+465*x*y-y=x^3, with discriminant -100544652. 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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