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curve #6043

y2 + xy + y = x3 − 11663347321x + 484821706426632
a-invariants
[1, 0, 1, -11663347321, 484821706426632]
c-invariants
[559840671385, -418886794113617341]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/3ℤ
conductor (N)
323607326
discriminant (Δ)
-647214652
Faltings height
3.7895
naive height
81.1528
primes of bad reduction
2, 7, 31, 97, 7687
regulator
1685.3292089388922916731005693232947009547439
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=865, b=-1 in y^2+a*x*y+b*y=x^3 gives y^2+865*x*y-y=x^3, with discriminant -647214652. 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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