Properties

Label 966.e
Number of curves $2$
Conductor $966$
CM no
Rank $1$
Graph

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

Elliptic curves in class 966.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
966.e1 966e2 \([1, 0, 1, -361, 2564]\) \(5182207647625/91449288\) \(91449288\) \([2]\) \(384\) \(0.32385\)  
966.e2 966e1 \([1, 0, 1, -1, 116]\) \(-15625/5842368\) \(-5842368\) \([2]\) \(192\) \(-0.022728\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 966.e have rank \(1\).

Complex multiplication

The elliptic curves in class 966.e do not have complex multiplication.

Modular form 966.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} - 2q^{11} + q^{12} - 6q^{13} + q^{14} + q^{16} + 2q^{17} - q^{18} - 6q^{19} + O(q^{20})\)  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.