Properties

Label 4864f
Number of curves $1$
Conductor $4864$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 4864f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4864.n1 4864f1 \([0, 1, 0, 3, -37]\) \(64/19\) \(-622592\) \([]\) \(512\) \(-0.20904\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4864f1 has rank \(0\).

Complex multiplication

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

Modular form 4864.2.a.f

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