Properties

Label 9450.z
Number of curves 3
Conductor 9450
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("9450.z1")
sage: E.isogeny_class()

Elliptic curves in class 9450.z

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
9450.z1 9450h3 [1, -1, 0, -42567, -13650409] 1 139968  
9450.z2 9450h1 [1, -1, 0, -4317, 110341] 1 15552 \(\Gamma_0(N)\)-optimal
9450.z3 9450h2 [1, -1, 0, 4683, 477341] 1 46656  

Rank

sage: E.rank()

The elliptic curves in class 9450.z have rank \(1\).

Modular form 9450.2.a.z

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

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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.