Properties

Label 186.c
Number of curves 2
Conductor 186
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("186.c1")
sage: E.isogeny_class()

Elliptic curves in class 186.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
186.c1 186b2 [1, 0, 0, -1395, -20181] 1 100  
186.c2 186b1 [1, 0, 0, 15, 9] 5 20 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 186.c have rank \(0\).

Modular form 186.2.a.c

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

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 LMFDB 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 LMFDB labels.