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curve #6034

y2 + y = x3 − 7247758464x + 237494568222722
a-invariants
[0, 0, 1, -7247758464, 237494568222722]
c-invariants
[347892406272, -205195306944432024]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/3ℤ
conductor (N)
1358954739
discriminant (Δ)
-12230592651
Faltings height
3.7077
naive height
79.7255
primes of bad reduction
3, 1549, 10831
regulator
795.85403819000025054523242646291858262408182
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=768, b=-3 in y^2+a*x*y+b*y=x^3 gives y^2+768*x*y-3*y=x^3, with discriminant -12230592651. 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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