# Properties

 Label 9450.cf Number of curves 2 Conductor 9450 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9450.cf1")
sage: E.isogeny_class()

## Elliptic curves in class 9450.cf

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
9450.cf1 9450df2 [1, -1, 1, -1355, 43647] 1 10368
9450.cf2 9450df1 [1, -1, 1, 145, -1353] 1 3456 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form9450.2.a.cf

sage: E.q_eigenform(10)
$$q + q^{2} + q^{4} - q^{7} + q^{8} - 3q^{11} + q^{13} - q^{14} + q^{16} - q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.