# Properties

 Label 4410l Number of curves 2 Conductor 4410 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4410.i1")

sage: E.isogeny_class()

## Elliptic curves in class 4410l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.i2 4410l1 [1, -1, 0, -31320, 2516800]  26880 $$\Gamma_0(N)$$-optimal
4410.i1 4410l2 [1, -1, 0, -525240, 146642656]  53760

## Rank

sage: E.rank()

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

## Modular form4410.2.a.i

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 