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curve #6366

y2 = x3 + x2 − 7467885199058505x + 4816608615579650078824128
a-invariants
[0, 1, 0, -7467885199058505, 4816608615579650078824128]
c-invariants
[358458489554808256, -4161549846011568605432896096]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/6ℤ
conductor (N)
1023993662229363540
discriminant (Δ)
-9995623783222345564516598373117516286221614892750000
Faltings height
8.6571
naive height
127.1914
primes of bad reduction
2, 3, 5, 11, 13, 17, 19, 41, 233, 911, 42457
regulator
101310.58423980365604939584651121194583786251892177
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=11883/42457. Clearing denominators gives the integral model [30574,-645722220,-27415428294540,0,0], 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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