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curve #3373

y2 + xy = x3 − 238726467x + 1419699746241
a-invariants
[1, 0, 0, -238726467, 1419699746241]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/9ℤ
conductor (N)
810894
discriminant (Δ)
-14517616550358266666496
Faltings height
3.4139
naive height
69.4861
primes of bad reduction
2, 3, 7, 43, 449
regulator
5.076247522799251002895404324525134830883
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 = -6/1; converted to the global minimal model. The 1 witness points were found with PARI/GP ellrank. Conductor 810894, torsion ℤ/9ℤ.

last edited by David Renshaw at · history

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