# Properties

 Label 9450.h Number of curves 3 Conductor 9450 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9450.h1")

sage: E.isogeny_class()

## Elliptic curves in class 9450.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9450.h1 9450f2 [1, -1, 0, -31767, -2171359] [] 23328
9450.h2 9450f1 [1, -1, 0, -267, -4859] [] 7776 $$\Gamma_0(N)$$-optimal
9450.h3 9450f3 [1, -1, 0, 2358, 118516] [] 23328

## Rank

sage: E.rank()

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

## Modular form9450.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{7} - q^{8} - 3q^{11} + 4q^{13} + q^{14} + q^{16} - 6q^{17} - 7q^{19} + O(q^{20})$$

## 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. 