Properties

Label 257600.cz
Number of curves $1$
Conductor $257600$
CM no
Rank $0$

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Show commands for: SageMath
sage: E = EllipticCurve("cz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 257600.cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.cz1 257600cz1 \([0, 0, 0, 17140, -17414640]\) \(84972077055/20040095362\) \(-131334768964403200\) \([]\) \(1548288\) \(1.9639\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257600.cz1 has rank \(0\).

Complex multiplication

The elliptic curves in class 257600.cz do not have complex multiplication.

Modular form 257600.2.a.cz

sage: E.q_eigenform(10)
 
\(q - q^{7} - 3q^{9} + 4q^{11} - 3q^{13} + q^{17} + O(q^{20})\)  Toggle raw display