Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("2310.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2310k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2310.j4 2310k1 [1, 0, 1, 192, -194] [2] 1536 \(\Gamma_0(N)\)-optimal
2310.j3 2310k2 [1, 0, 1, -788, -1762] [2, 2] 3072  
2310.j1 2310k3 [1, 0, 1, -9538, -358762] [2] 6144  
2310.j2 2310k4 [1, 0, 1, -7718, 258806] [2] 6144  

Rank

sage: E.rank()
 

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

Modular form 2310.2.a.j

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

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.