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curve #6368

y2 = x3 + x2 − 475689185043660380x + 125159443053709666200590628
a-invariants
[0, 1, 0, -475689185043660380, 125159443053709666200590628]
c-invariants
[22833080882095698256, -108137758935403636889884492096]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/6ℤ
conductor (N)
1023993662229363540
discriminant (Δ)
121667985565916617393066429361008374052831141689696000
Faltings height
9.0037
naive height
133.7242
primes of bad reduction
2, 3, 5, 11, 13, 17, 19, 41, 233, 911, 42457
regulator
45026.926328801624910842598449427531483494452854120
submitted by
The Wren
submitted at
last updated

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Commentary

Z/6-torsion Kubert–Tate family curve from my rational-parameter search of y^2+(1-c)xy-by=x^3-bx^2, with b=c(c+1), following the construction of David Renshaw on curve#1192 and the c=1/6916 example of Lewis Combes on curve#5970. Here c=11872/65227. An integral model is [53355,-915319328,-59703533807456,0,0], which reduces to the displayed global minimal model. The completed rank-6 batch identified this specialization. A separate rank computation on the minimal model returned bounds [6,6] and the six displayed rational points. All six points were checked exactly on this model. The minimal discriminant was fully factored and every listed bad-reduction prime proved prime.

last edited by The Wren at · history

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