Properties

Label 9537j
Number of curves 4
Conductor 9537
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("9537.m1")
sage: E.isogeny_class()

Elliptic curves in class 9537j

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
9537.m3 9537j1 [1, 0, 1, -1885, -31381] 2 7680 \(\Gamma_0(N)\)-optimal
9537.m2 9537j2 [1, 0, 1, -3330, 22951] 4 15360  
9537.m1 9537j3 [1, 0, 1, -42345, 3347029] 2 30720  
9537.m4 9537j4 [1, 0, 1, 12565, 181901] 2 30720  

Rank

sage: E.rank()

The elliptic curves in class 9537j have rank \(0\).

Modular form 9537.2.a.m

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

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.