# Properties

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

# Related objects

Show commands: SageMath
E = EllipticCurve("bq1")

E.isogeny_class()

## Elliptic curves in class 4800.bq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.bq1 4800bf1 $$[0, 1, 0, -33, -87]$$ $$-102400/3$$ $$-120000$$ $$[]$$ $$480$$ $$-0.24652$$ $$\Gamma_0(N)$$-optimal
4800.bq2 4800bf2 $$[0, 1, 0, 167, 3713]$$ $$20480/243$$ $$-6075000000$$ $$[]$$ $$2400$$ $$0.55819$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4800.2.a.bq

sage: E.q_eigenform(10)

$$q + q^{3} - 3 q^{7} + q^{9} - 2 q^{11} - q^{13} + 2 q^{17} + 5 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.