Properties

Label 2310.e
Number of curves $2$
Conductor $2310$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2310.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.e1 2310e1 \([1, 0, 1, -169, -724]\) \(529278808969/88704000\) \(88704000\) \([2]\) \(960\) \(0.24613\) \(\Gamma_0(N)\)-optimal
2310.e2 2310e2 \([1, 0, 1, 311, -3988]\) \(3342032927351/8893500000\) \(-8893500000\) \([2]\) \(1920\) \(0.59271\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2310.e have rank \(0\).

Complex multiplication

The elliptic curves in class 2310.e do not have complex multiplication.

Modular form 2310.2.a.e

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.