Properties

Label 180336.z
Number of curves $1$
Conductor $180336$
CM no
Rank $1$

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

Elliptic curves in class 180336.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
180336.z1 180336cy1 \([0, -1, 0, -640, 6448]\) \(98116996/39\) \(11541504\) \([]\) \(39168\) \(0.31913\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 180336.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 180336.z do not have complex multiplication.

Modular form 180336.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} + q^{9} - 2 q^{11} - q^{13} - q^{15} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display