# Properties

 Label 9450.dl Number of curves 2 Conductor 9450 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9450.dl1")

sage: E.isogeny_class()

## Elliptic curves in class 9450.dl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9450.dl1 9450dw2 [1, -1, 1, -3368930, -2317366303]  388800
9450.dl2 9450dw1 [1, -1, 1, -3344555, -2353430053] [] 129600 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form9450.2.a.dl

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{7} + q^{8} - 7q^{13} + q^{14} + q^{16} - 3q^{17} - q^{19} + O(q^{20})$$

## 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. 