Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4864.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4864.e1 4864o1 \([0, -1, 0, 147, 181]\) \(10648000/6859\) \(-224755712\) \([]\) \(1152\) \(0.29147\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4864.e1 has rank \(1\).

Complex multiplication

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

Modular form 4864.2.a.e

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