Properties

Label 2310.l
Number of curves 8
Conductor 2310
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("2310.l1")
sage: E.isogeny_class()

Elliptic curves in class 2310.l

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
2310.l1 2310l7 [1, 0, 1, -256428, 46871746] 2 27648  
2310.l2 2310l4 [1, 0, 1, -252003, 48670756] 6 9216  
2310.l3 2310l6 [1, 0, 1, -50628, -3508094] 4 13824  
2310.l4 2310l3 [1, 0, 1, -47748, -4019582] 2 6912  
2310.l5 2310l2 [1, 0, 1, -15753, 759256] 12 4608  
2310.l6 2310l5 [1, 0, 1, -12783, 1055068] 6 9216  
2310.l7 2310l1 [1, 0, 1, -1173, 6928] 6 2304 \(\Gamma_0(N)\)-optimal
2310.l8 2310l8 [1, 0, 1, 109092, -21141182] 2 27648  

Rank

sage: E.rank()

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

Modular form 2310.2.a.l

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.