# Properties

 Label 162240fz Number of curves $2$ Conductor $162240$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fz1")

sage: E.isogeny_class()

## Elliptic curves in class 162240fz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162240.eu2 162240fz1 $$[0, 1, 0, 43039, -9524865]$$ $$6967871/35100$$ $$-44412697549209600$$ $$$$ $$1548288$$ $$1.8766$$ $$\Gamma_0(N)$$-optimal
162240.eu1 162240fz2 $$[0, 1, 0, -497761, -121254145]$$ $$10779215329/1232010$$ $$1558885683977256960$$ $$$$ $$3096576$$ $$2.2232$$

## Rank

sage: E.rank()

The elliptic curves in class 162240fz have rank $$0$$.

## Complex multiplication

The elliptic curves in class 162240fz do not have complex multiplication.

## Modular form 162240.2.a.fz

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - 2q^{7} + q^{9} + 4q^{11} - q^{15} + 8q^{17} - 6q^{19} + O(q^{20})$$ ## 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 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. 