# Properties

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

# Related objects

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 form9450.2.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.