# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9450.cl1")
sage: E.isogeny_class()

## Elliptic curves in class 9450.cl

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
9450.cl1 9450dd3 [1, -1, 1, -26555, 1672197] 1 15552
9450.cl2 9450dd1 [1, -1, 1, -305, 2697] 1 5184 $$\Gamma_0(N)$$-optimal
9450.cl3 9450dd2 [1, -1, 1, 2320, -27053] 1 15552

## Rank

sage: E.rank()

The elliptic curves in class 9450.cl have rank $$1$$.

## Modular form9450.2.a.cl

sage: E.q_eigenform(10)
$$q + q^{2} + q^{4} - q^{7} + q^{8} - 5q^{13} - q^{14} + q^{16} + 3q^{17} + 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.