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Properties

Label 2766.i
Number of curves $2$
Conductor $2766$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2766.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2766.i1 2766i2 \([1, 0, 0, -2365, -1318171]\) \(-1462947106919761/749561251618836\) \(-749561251618836\) \([]\) \(11200\) \(1.5333\)  
2766.i2 2766i1 \([1, 0, 0, -1105, 16169]\) \(-149222774347921/27874907136\) \(-27874907136\) \([5]\) \(2240\) \(0.72859\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2766.i have rank \(0\).

Complex multiplication

The elliptic curves in class 2766.i do not have complex multiplication.

Modular form 2766.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + 3 q^{7} + q^{8} + q^{9} + q^{10} - 3 q^{11} + q^{12} + 4 q^{13} + 3 q^{14} + q^{15} + q^{16} + 3 q^{17} + q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.