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curve #4883

y2 = x3 + 9320836232292484x
a-invariants
[0, 0, 0, 9320836232292484, 0]
c-invariants
[-447400139150039232, 0]
rank (lower bound)
≥ 5
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
74566689858339872
discriminant (Δ)
-51825631934990456881060927817683752112820840697856
Faltings height
8.2288
naive height
121.9267
primes of bad reduction
2, 23, 31, 79, 857
regulator
7536315.77460799103724110608536719228108926902754
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained by a rational 2-isogeny from curve #4720, 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. Five 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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