# Properties

 Label 4410.k Number of curves 4 Conductor 4410 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4410.k1")

sage: E.isogeny_class()

## Elliptic curves in class 4410.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.k1 4410c4 [1, -1, 0, -56310, 5157116]  17280
4410.k2 4410c3 [1, -1, 0, -3390, 87380]  8640
4410.k3 4410c2 [1, -1, 0, -1185, -3809]  5760
4410.k4 4410c1 [1, -1, 0, 285, -575]  2880 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form4410.2.a.k

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 