Properties

Label 110c
Number of curves 2
Conductor 110
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("110.a1")
sage: E.isogeny_class()

Elliptic curves in class 110c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
110.a1 110c1 [1, 0, 1, -89, 316] 3 28 \(\Gamma_0(N)\)-optimal
110.a2 110c2 [1, 0, 1, 296, 1702] 1 84  

Rank

sage: E.rank()

The elliptic curves in class 110c have rank \(0\).

Modular form 110.2.a.a

sage: E.q_eigenform(10)
\( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 5q^{7} - q^{8} - 2q^{9} + q^{10} + q^{11} + q^{12} + 2q^{13} - 5q^{14} - q^{15} + q^{16} + 3q^{17} + 2q^{18} - 7q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.