Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("2310.u1")
sage: E.isogeny_class()

Elliptic curves in class 2310t

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
2310.u8 2310t1 [1, 0, 0, 1589, 3185] 6 3456 \(\Gamma_0(N)\)-optimal
2310.u7 2310t2 [1, 0, 0, -6411, 23985] 12 6912  
2310.u6 2310t3 [1, 0, 0, -20251, -1219519] 2 10368  
2310.u5 2310t4 [1, 0, 0, -65811, -6474375] 6 13824  
2310.u4 2310t5 [1, 0, 0, -75011, 7885545] 6 13824  
2310.u3 2310t6 [1, 0, 0, -332751, -73907019] 4 20736  
2310.u1 2310t7 [1, 0, 0, -5324001, -4728746769] 2 41472  
2310.u2 2310t8 [1, 0, 0, -341501, -69817269] 2 41472  

Rank

sage: E.rank()

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

Modular form 2310.2.a.u

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.