Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("110.b1")
sage: E.isogeny_class()

Elliptic curves in class 110a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
110.b2 110a1 [1, 1, 1, 10, -45] 5 20 \(\Gamma_0(N)\)-optimal
110.b1 110a2 [1, 1, 1, -5940, -178685] 1 100  

Rank

sage: E.rank()

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

Modular form 110.2.a.b

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.