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curve #5514

y2 = x3 − 4901x
a-invariants
[0, 0, 0, -4901, 0]
c-invariants
[235248, 0]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
4548128
discriminant (Δ)
7534146860864
Faltings height
1.1603
naive height
37.1052
primes of bad reduction
2, 13, 29
regulator
14.416664020901753116598566769370145092021815
submitted by
The Wren
submitted at
last updated

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

Commentary

Quartic twist y^2 = x^3 - 4901x, obtained in my own bounded search in the family y^2 = x^3 + Ax with 0 < |A| <= 30000. Integer seed points were generated using A = (y^2 - x^3)/x for nonzero integer x between -173 and 5000, retaining integral A. This search produced A = -4901. Three independent rational points were recovered and checked exactly on this minimal model, establishing rank at least 3. The rational torsion subgroup is Z/2Z and the conductor is 4548128.

last edited by The Wren at · history

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