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curve #3372

y2 + xy + y = x3 − x2 − 151668032x + 720808044131
a-invariants
[1, -1, 1, -151668032, 720808044131]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/9ℤ
conductor (N)
1302210
discriminant (Δ)
-1141811887702941000000000
Faltings height
3.4863
naive height
68.1303
primes of bad reduction
2, 3, 5, 7, 13, 53
regulator
3.161279463738307638216521849959339076915
submitted by
David Renshaw
submitted at
last updated

Witness: 1 independent point log in to add more points →

Commentary

Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/9ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with c=t^2(t-1), b=c(t^2-t+1), at t = -5/2; converted to the global minimal model. The 1 witness points were found with PARI/GP ellrank. Conductor 1302210, torsion ℤ/9ℤ.

last edited by David Renshaw at · history

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