Properties

Label 4864.k
Number of curves $1$
Conductor $4864$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4864.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4864.k1 4864n1 \([0, 1, 0, 1, 5]\) \(64/19\) \(-9728\) \([]\) \(256\) \(-0.55561\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4864.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 4864.k do not have complex multiplication.

Modular form 4864.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{5} + q^{7} - 2q^{9} + 4q^{11} - q^{13} - 2q^{15} - 5q^{17} + q^{19} + O(q^{20})\)  Toggle raw display