# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bn1")

sage: E.isogeny_class()

## Elliptic curves in class 4800.bn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.bn1 4800bg1 $$[0, 1, 0, -53, 123]$$ $$131072/9$$ $$1152000$$ $$[2]$$ $$768$$ $$-0.088679$$ $$\Gamma_0(N)$$-optimal
4800.bn2 4800bg2 $$[0, 1, 0, 47, 623]$$ $$5488/81$$ $$-165888000$$ $$[2]$$ $$1536$$ $$0.25789$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4800.2.a.bn

sage: E.q_eigenform(10)

$$q + q^{3} - 4q^{7} + q^{9} + 4q^{11} - 4q^{17} + O(q^{20})$$

## 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.