Properties

Label 46746.z
Number of curves $1$
Conductor $46746$
CM no
Rank $1$

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

Elliptic curves in class 46746.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46746.z1 46746bz1 \([1, -1, 1, -3317, 75485]\) \(-47045881/848\) \(-72729670608\) \([]\) \(92160\) \(0.88054\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 46746.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 46746.z do not have complex multiplication.

Modular form 46746.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 4 q^{5} + q^{8} - 4 q^{10} + 4 q^{11} - q^{13} + q^{16} + 5 q^{17} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display