# Properties

 Label 4800.cr Number of curves $2$ Conductor $4800$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cr1")

sage: E.isogeny_class()

## Elliptic curves in class 4800.cr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.cr1 4800cq2 $$[0, 1, 0, -53833, 4789463]$$ $$2156689088/81$$ $$648000000000$$ $$$$ $$15360$$ $$1.3528$$
4800.cr2 4800cq1 $$[0, 1, 0, -3208, 81338]$$ $$-29218112/6561$$ $$-820125000000$$ $$$$ $$7680$$ $$1.0062$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4800.cr have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4800.cr do not have complex multiplication.

## Modular form4800.2.a.cr

sage: E.q_eigenform(10)

$$q + q^{3} + 4 q^{7} + q^{9} + 4 q^{13} + 8 q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 