Properties

Label 550.j
Number of curves 3
Conductor 550
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("550.j1")
sage: E.isogeny_class()

Elliptic curves in class 550.j

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
550.j1 550k3 [1, 1, 1, -30328, 2020281] 5 1200  
550.j2 550k1 [1, 1, 1, -28, -69] 1 48 \(\Gamma_0(N)\)-optimal
550.j3 550k2 [1, 1, 1, 197, 681] 5 240  

Rank

sage: E.rank()

The elliptic curves in class 550.j have rank \(0\).

Modular form 550.2.a.j

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.