# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("4410.h1")

sage: E.isogeny_class()

## Elliptic curves in class 4410i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.h1 4410i1 [1, -1, 0, -1185, 16001] [] 1680 $$\Gamma_0(N)$$-optimal
4410.h2 4410i2 [1, -1, 0, 8265, -151075] [] 11760

## Rank

sage: E.rank()

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

## Modular form4410.2.a.h

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 