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Properties

Label 966.i
Number of curves $2$
Conductor $966$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 966.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
966.i1 966k2 \([1, 0, 0, -27, -249]\) \(-2181825073/25039686\) \(-25039686\) \([]\) \(360\) \(0.10160\)  
966.i2 966k1 \([1, 0, 0, 3, 9]\) \(2924207/34776\) \(-34776\) \([3]\) \(120\) \(-0.44771\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 966.i have rank \(0\).

Complex multiplication

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

Modular form 966.2.a.i

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.