Properties

Label 660.a
Number of curves $2$
Conductor $660$
CM no
Rank $0$
Graph

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

Elliptic curves in class 660.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
660.a1 660a2 \([0, -1, 0, -396, -2904]\) \(26894628304/9075\) \(2323200\) \([2]\) \(192\) \(0.19367\)  
660.a2 660a1 \([0, -1, 0, -21, -54]\) \(-67108864/61875\) \(-990000\) \([2]\) \(96\) \(-0.15290\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 660.a have rank \(0\).

Complex multiplication

The elliptic curves in class 660.a do not have complex multiplication.

Modular form 660.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2 q^{7} + q^{9} - q^{11} + 2 q^{13} + q^{15} + 8 q^{17} - 2 q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.