# Properties

 Label 4410.bg Number of curves $2$ Conductor $4410$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("4410.bg1")

sage: E.isogeny_class()

## Elliptic curves in class 4410.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.bg1 4410bl2 [1, -1, 1, -1427, -35661] [] 6048
4410.bg2 4410bl1 [1, -1, 1, 148, 879] [] 2016 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4410.bg have rank $$1$$.

## Modular form4410.2.a.bg

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} - 3q^{11} + q^{13} + q^{16} - 6q^{17} + q^{19} + O(q^{20})$$

## 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.