Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 966.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
966.b1 966a2 \([1, 1, 0, -3346, 63700]\) \(4144806984356137/568114785504\) \(568114785504\) \([2]\) \(1920\) \(0.98234\)  
966.b2 966a1 \([1, 1, 0, 334, 5556]\) \(4101378352343/15049939968\) \(-15049939968\) \([2]\) \(960\) \(0.63576\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 966.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 2q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + 2q^{10} - q^{12} + 4q^{13} + q^{14} + 2q^{15} + q^{16} - q^{18} + 6q^{19} + O(q^{20})\)  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.