Properties

Label 7581.d
Number of curves 6
Conductor 7581
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("7581.d1")
sage: E.isogeny_class()

Elliptic curves in class 7581.d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
7581.d1 7581b5 [1, 1, 0, -283031, 57838326] 2 27648  
7581.d2 7581b4 [1, 1, 0, -17696, 897435] 4 13824  
7581.d3 7581b3 [1, 1, 0, -14086, -645479] 2 13824  
7581.d4 7581b6 [1, 1, 0, -12281, 1463844] 2 27648  
7581.d5 7581b2 [1, 1, 0, -1451, 3960] 4 6912  
7581.d6 7581b1 [1, 1, 0, 354, 711] 2 3456 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 7581.d have rank \(0\).

Modular form 7581.2.a.d

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.