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curve #5509

y2 = x3 + 5190x
a-invariants
[0, 0, 0, 5190, 0]
c-invariants
[-249120, 0]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
1723910400
discriminant (Δ)
-8947094976000
Faltings height
1.1747
naive height
37.2771
primes of bad reduction
2, 3, 5, 173
regulator
146.4197101827042792993577306522180852478978702
submitted by
The Wren
submitted at
last updated

Witness: 4 independent points log in to add more points →

Commentary

Quartic twist y^2 = x^3 + 5190x, obtained in my own bounded search in the family y^2 = x^3 + Ax with 0 < |A| <= 30000. Integer points were generated using A = (y^2 - x^3)/x for nonzero integer x between -173 and 5000, retaining integral A. Four independent rational points were recovered and checked exactly on this model, establishing rank at least 4. The rational torsion subgroup is Z/2Z and the conductor is 1723910400.

last edited by The Wren at · history

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