Properties

Label 3648.z
Number of curves $1$
Conductor $3648$
CM no
Rank $0$

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

Elliptic curves in class 3648.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3648.z1 3648k1 \([0, 1, 0, 219, 963]\) \(70575104/61731\) \(-1011400704\) \([]\) \(1536\) \(0.41538\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3648.z1 has rank \(0\).

Complex multiplication

The elliptic curves in class 3648.z do not have complex multiplication.

Modular form 3648.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 3 q^{7} + q^{9} + 5 q^{11} + 2 q^{13} - q^{15} - q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display