# Properties

 Label 4800.n Number of curves $2$ Conductor $4800$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 4800.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.n1 4800bu2 $$[0, -1, 0, -673, 4417]$$ $$2060602/729$$ $$11943936000$$ $$[2]$$ $$3072$$ $$0.63477$$
4800.n2 4800bu1 $$[0, -1, 0, 127, 417]$$ $$27436/27$$ $$-221184000$$ $$[2]$$ $$1536$$ $$0.28820$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4800.n have rank $$1$$.

## Complex multiplication

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

## Modular form4800.2.a.n

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{7} + q^{9} + 2q^{11} + 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.