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Properties

Label 404928.z
Number of curves $1$
Conductor $404928$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("z1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 404928.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 404928.z do not have complex multiplication.

Modular form 404928.2.a.z

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{5} - q^{7} + 5 q^{13} + 7 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 404928.z

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
404928.z1 404928z1 \([0, 0, 0, -10956, 1291376]\) \(-761048497/3329408\) \(-636259777118208\) \([]\) \(1290240\) \(1.5255\) \(\Gamma_0(N)\)-optimal