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curve #6348

y2 + xy + y = x3 − 106853490994139x + 425139223106776471986
a-invariants
[1, 0, 1, -106853490994139, 425139223106776471986]
c-invariants
[5128967567718649, -367320296457706223374093]
rank (lower bound)
≥ 5
torsion subgroup
ℤ/6ℤ
conductor (N)
71020124709730
discriminant (Δ)
1135567536855015663138280717529656100
Faltings height
6.5051
naive height
108.5210
primes of bad reduction
2, 5, 7, 17, 31, 281, 883, 7759
regulator
2946.18442564883709010143982079541059128391451251
submitted by
The Wren
submitted at
last updated

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Commentary

Z/6-torsion Kubert–Tate family curve from a rational-parameter search of the family y^2+(1-c)xy-by=x^3-bx^2 with c=a/d, b=c(c+1), following the construction of David Renshaw on curve #1192 and the t=1/6916 example of Lewis Combes on curve #5970. The search covered coprime pairs (a,d) with log|Δ_min| ≤ 88.12, ranked by discriminant. Rank ≥ 5 certified: 5 independent rational points, checked exactly (independent mod 5 and mod 7); PARI ellrank bounds 5 5. The rational torsion subgroup is Z/6Z.

last edited by The Wren at · history

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