# Properties

 Label 4410.r Number of curves $2$ Conductor $4410$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4410.r1")

sage: E.isogeny_class()

## Elliptic curves in class 4410.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.r1 4410n1 [1, -1, 0, -58074, -5372200] [] 11760 $$\Gamma_0(N)$$-optimal
4410.r2 4410n2 [1, -1, 0, 404976, 51008768] [] 82320

## Rank

sage: E.rank()

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

## Modular form4410.2.a.r

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 LMFDB 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 LMFDB labels. 