# Properties

 Label 9338f Number of curves $2$ Conductor $9338$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 9338f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9338.g2 9338f1 $$[1, 0, 0, 92, 0]$$ $$86058173375/49827568$$ $$-49827568$$ $$$$ $$2688$$ $$0.16647$$ $$\Gamma_0(N)$$-optimal
9338.g1 9338f2 $$[1, 0, 0, -368, -92]$$ $$5512402554625/3188422748$$ $$3188422748$$ $$$$ $$5376$$ $$0.51304$$

## Rank

sage: E.rank()

The elliptic curves in class 9338f have rank $$1$$.

## Complex multiplication

The elliptic curves in class 9338f do not have complex multiplication.

## Modular form9338.2.a.f

sage: E.q_eigenform(10)

$$q + q^{2} - 2q^{3} + q^{4} - 2q^{6} - q^{7} + q^{8} + q^{9} + 4q^{11} - 2q^{12} - 2q^{13} - q^{14} + q^{16} + 4q^{17} + q^{18} + O(q^{20})$$ ## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 