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curve #6046

y2 = x3 + x2 − 71453202x + 232453539361
a-invariants
[0, 1, 0, -71453202, 232453539361]
c-invariants
[3429753712, -200860436530144]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/3ℤ
conductor (N)
28345084
discriminant (Δ)
-113380336
Faltings height
2.6415
naive height
65.8673
primes of bad reduction
2, 43, 223, 739
regulator
242.84693806529205041609386851667594614549086
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=242, b=-2 in y^2+a*x*y+b*y=x^3 gives y^2+242*x*y-2*y=x^3, with discriminant -113380336. 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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