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curve #4882

y2 = x3 + 393129x
a-invariants
[0, 0, 0, 393129, 0]
c-invariants
[-18870192, 0]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
25160256
discriminant (Δ)
-3888527896632684096
Faltings height
2.2565
naive height
50.2593
primes of bad reduction
2, 3, 11, 19
regulator
181.50451538917888451956276892179582939838190
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained by a rational 2-isogeny from curve #4719, submitted by David Renshaw and sourced to Table 2 of Watkins, Donnelly, Elkies, Fisher, Granville and Rogers, Ranks of quadratic twists of elliptic curves (2014): https://doi.org/10.5802/pmb.9. Three rational points transported through the isogeny and checked exactly. Rational torsion C2. Same rank and conductor as the source. Source-attributed existing curve.

last edited by The Wren at · history

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