Properties

Label 864.a
Number of curves $1$
Conductor $864$
CM no
Rank $0$

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

Elliptic curves in class 864.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
864.a1 864i1 \([0, 0, 0, -216, -1296]\) \(-13824\) \(-80621568\) \([]\) \(288\) \(0.26670\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 864.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 864.a do not have complex multiplication.

Modular form 864.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - 3 q^{7} + 6 q^{11} - 3 q^{13} + 2 q^{17} + 3 q^{19} + O(q^{20})\)  Toggle raw display