# Properties

 Label 4410.v Number of curves $2$ Conductor $4410$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 4410.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.v1 4410bg1 $$[1, -1, 1, -471218, -70884943]$$ $$393349474783/153600000$$ $$4518570931660800000$$ $$[2]$$ $$125440$$ $$2.2783$$ $$\Gamma_0(N)$$-optimal
4410.v2 4410bg2 $$[1, -1, 1, 1504462, -511856719]$$ $$12801408679457/11250000000$$ $$-330950019408750000000$$ $$[2]$$ $$250880$$ $$2.6248$$

## Rank

sage: E.rank()

The elliptic curves in class 4410.v have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4410.v do not have complex multiplication.

## Modular form4410.2.a.v

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.