# Properties

 Label 4410d Number of curves 4 Conductor 4410 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4410.p1")

sage: E.isogeny_class()

## Elliptic curves in class 4410d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.p2 4410d1 [1, -1, 0, -5154, -140960] [2] 4608 $$\Gamma_0(N)$$-optimal
4410.p3 4410d2 [1, -1, 0, -3684, -224162] [2] 9216
4410.p1 4410d3 [1, -1, 0, -20589, 1001573] [2] 13824
4410.p4 4410d4 [1, -1, 0, 32331, 5266925] [2] 27648

## Rank

sage: E.rank()

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

## Modular form4410.2.a.p

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.