Properties

Label 2310h
Number of curves 4
Conductor 2310
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2310.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2310h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2310.g3 2310h1 [1, 0, 1, -74, 236] [2] 512 \(\Gamma_0(N)\)-optimal
2310.g2 2310h2 [1, 0, 1, -94, 92] [2, 2] 1024  
2310.g1 2310h3 [1, 0, 1, -864, -9764] [2] 2048  
2310.g4 2310h4 [1, 0, 1, 356, 812] [2] 2048  

Rank

sage: E.rank()
 

The elliptic curves in class 2310h have rank \(1\).

Modular form 2310.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - q^{11} + q^{12} - 6q^{13} - q^{14} - q^{15} + q^{16} + 2q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.