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curve #3387

y2 + xy + y = x3 − x2 − 1234164209x + 16688478890657
a-invariants
[1, -1, 1, -1234164209, 16688478890657]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/9ℤ
conductor (N)
524286
discriminant (Δ)
-658995091276965605277696
Faltings height
3.7953
naive height
74.4146
primes of bad reduction
2, 3, 7, 19, 73
regulator
4.916870444873368745290116405034967251162
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 = 1/8; converted to the global minimal model. The 1 witness points were found with PARI/GP ellrank. Conductor 524286, torsion ℤ/9ℤ.

last edited by David Renshaw at · history

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