Properties

Label 190575.cz
Number of curves $1$
Conductor $190575$
CM no
Rank $1$

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

Elliptic curves in class 190575.cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190575.cz1 190575dy1 \([1, -1, 0, 81108, 49107141]\) \(24167/441\) \(-1076781598340765625\) \([]\) \(2737152\) \(2.1405\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 190575.cz1 has rank \(1\).

Complex multiplication

The elliptic curves in class 190575.cz do not have complex multiplication.

Modular form 190575.2.a.cz

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - q^{7} - 3 q^{8} - 7 q^{13} - q^{14} - q^{16} + 3 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display