# Properties

 Label 4800.bq Number of curves 2 Conductor 4800 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4800.bq1")

sage: E.isogeny_class()

## Elliptic curves in class 4800.bq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4800.bq1 4800bf1 [0, 1, 0, -33, -87] [] 480 $$\Gamma_0(N)$$-optimal
4800.bq2 4800bf2 [0, 1, 0, 167, 3713] [] 2400

## Rank

sage: E.rank()

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

## Modular form4800.2.a.bq

sage: E.q_eigenform(10)

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

## 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. 