Properties

Label 11913i
Number of curves 4
Conductor 11913
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("11913.d1")
sage: E.isogeny_class()

Elliptic curves in class 11913i

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
11913.d3 11913i1 [1, 0, 0, -2354, 43395] 2 10800 \(\Gamma_0(N)\)-optimal
11913.d2 11913i2 [1, 0, 0, -4159, -32776] 4 21600  
11913.d1 11913i3 [1, 0, 0, -52894, -4682095] 2 43200  
11913.d4 11913i4 [1, 0, 0, 15696, -251181] 2 43200  

Rank

sage: E.rank()

The elliptic curves in class 11913i have rank \(0\).

Modular form 11913.2.a.d

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

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.