# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("4410.c1")

sage: E.isogeny_class()

## Elliptic curves in class 4410.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.c1 4410k2 [1, -1, 0, -216540, -38731694] [] 30240
4410.c2 4410k1 [1, -1, 0, -450, -138020] [] 10080 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form4410.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 3q^{11} - 5q^{13} + q^{16} + 6q^{17} + q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 