Properties

Label 258570.cz
Number of curves $1$
Conductor $258570$
CM no
Rank $1$

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

Elliptic curves in class 258570.cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
258570.cz1 258570cz1 \([1, -1, 1, -217028, 39192391]\) \(-2010964662603/13363360\) \(-7512428815987680\) \([]\) \(3225600\) \(1.8818\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 258570.cz1 has rank \(1\).

Complex multiplication

The elliptic curves in class 258570.cz do not have complex multiplication.

Modular form 258570.2.a.cz

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - 4 q^{7} + q^{8} - q^{10} - q^{11} - 4 q^{14} + q^{16} + q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display