Properties

Label 4864.a
Number of curves $1$
Conductor $4864$
CM no
Rank $2$

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4864.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4864.a1 4864l1 \([0, 0, 0, -22, 40]\) \(-2299968/19\) \(-9728\) \([]\) \(960\) \(-0.40811\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4864.a1 has rank \(2\).

Complex multiplication

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

Modular form 4864.2.a.a

sage: E.q_eigenform(10)
 
\(q - 3q^{3} - 4q^{5} + q^{7} + 6q^{9} - 5q^{13} + 12q^{15} - 5q^{17} - q^{19} + O(q^{20})\)  Toggle raw display