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Properties

Label 2366.l
Number of curves $2$
Conductor $2366$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 2366.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2366.l1 2366n1 \([1, 1, 1, -2792, -60897]\) \(-226981/14\) \(-148462991222\) \([]\) \(3120\) \(0.89805\) \(\Gamma_0(N)\)-optimal
2366.l2 2366n2 \([1, 1, 1, 8193, 3625669]\) \(5735339/537824\) \(-5703354270784352\) \([]\) \(15600\) \(1.7028\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2366.l have rank \(1\).

Complex multiplication

The elliptic curves in class 2366.l do not have complex multiplication.

Modular form 2366.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 2 q^{5} - q^{6} - q^{7} + q^{8} - 2 q^{9} + 2 q^{10} - 5 q^{11} - q^{12} - q^{14} - 2 q^{15} + q^{16} + 2 q^{17} - 2 q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.