# Properties

 Label 4410v Number of curves $4$ Conductor $4410$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4410.y1")

sage: E.isogeny_class()

## Elliptic curves in class 4410v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.y3 4410v1 [1, -1, 1, -2288, -36333] [2] 4608 $$\Gamma_0(N)$$-optimal
4410.y4 4410v2 [1, -1, 1, 3592, -196269] [2] 9216
4410.y1 4410v3 [1, -1, 1, -46388, 3852307] [2] 13824
4410.y2 4410v4 [1, -1, 1, -33158, 6085531] [2] 27648

## Rank

sage: E.rank()

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

## Modular form4410.2.a.y

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.