Properties

Label 86640.z
Number of curves $1$
Conductor $86640$
CM no
Rank $1$

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

Elliptic curves in class 86640.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86640.z1 86640cl1 \([0, -1, 0, 3490, 178227]\) \(2253933824/7971615\) \(-16621901414640\) \([]\) \(168480\) \(1.2198\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 86640.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 86640.z do not have complex multiplication.

Modular form 86640.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 4 q^{7} + q^{9} - 2 q^{11} - 2 q^{13} - q^{15} + q^{17} + O(q^{20})\) Copy content Toggle raw display