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curve #1186

y2 + y = x3 + x2 − 552000x + 220315304
a-invariants
[0, 1, 1, -552000, 220315304]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/5ℤ
conductor (N)
2266095
discriminant (Δ)
-10239213052529296875
Faltings height
2.3513
naive height
51.9460
primes of bad reduction
3, 5, 13, 11621
regulator
10.481588762531397206393178706812492884475615
submitted by
David Renshaw
submitted at
last updated

Witness: 3 independent points log in to add more points →

Commentary

Found by a rational-parameter search of the Kubert-Tate family for torsion 5, at t=-39/25. In y^2+(1-c)xy-by=x^3-bx^2 the parameters are defined by c=t;b=t; Converted to the global minimal model; PARI/GP ellrank returned bounds [3,3]. The 3 supplied points and the torsion subgroup are independently certified by the site.

last edited by David Renshaw at · history

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