Properties

Label 834.g
Number of curves 2
Conductor 834
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("834.g1")
sage: E.isogeny_class()

Elliptic curves in class 834.g

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
834.g1 834g2 [1, 0, 0, -1090, -40504] 1 2000  
834.g2 834g1 [1, 0, 0, -70, 356] 5 400 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 834.g have rank \(1\).

Modular form 834.2.a.g

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

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.