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Properties

Label 11.a
Number of curves 3
Conductor 11
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("11.a1")
sage: E.isogeny_class()

Elliptic curves in class 11.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
11.a1 11a2 [0, -1, 1, -7820, -263580] 1 5  
11.a2 11a1 [0, -1, 1, -10, -20] 5 1 \(\Gamma_0(N)\)-optimal
11.a3 11a3 [0, -1, 1, 0, 0] 5 5  

Rank

sage: E.rank()

The elliptic curves in class 11.a have rank \(0\).

Modular form 11.2.a.a

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

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.