# Properties

 Label 5610.bg Number of curves $2$ Conductor $5610$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("bg1")

E.isogeny_class()

## Elliptic curves in class 5610.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.bg1 5610bf2 $$[1, 0, 0, -11764986, -15533261340]$$ $$-180093466903641160790448289/4344384000$$ $$-4344384000$$ $$[]$$ $$136080$$ $$2.2968$$
5610.bg2 5610bf1 $$[1, 0, 0, -145146, -21349404]$$ $$-338173143620095981729/979226371031040$$ $$-979226371031040$$ $$[3]$$ $$45360$$ $$1.7475$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5610.bg have rank $$0$$.

## Complex multiplication

The elliptic curves in class 5610.bg do not have complex multiplication.

## Modular form5610.2.a.bg

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} - q^{7} + q^{8} + q^{9} - q^{10} - q^{11} + q^{12} - 4 q^{13} - q^{14} - q^{15} + q^{16} + q^{17} + q^{18} - 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.