# Properties

 Label 20181d Number of curves 6 Conductor 20181 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("20181.e1")

sage: E.isogeny_class()

## Elliptic curves in class 20181d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20181.e6 20181d1 [1, 1, 1, 941, 2840] [2] 15360 $$\Gamma_0(N)$$-optimal
20181.e5 20181d2 [1, 1, 1, -3864, 18216] [2, 2] 30720
20181.e3 20181d3 [1, 1, 1, -37499, -2793670] [2] 61440
20181.e2 20181d4 [1, 1, 1, -47109, 3910266] [2, 2] 61440
20181.e1 20181d5 [1, 1, 1, -753444, 251410050] [2] 122880
20181.e4 20181d6 [1, 1, 1, -32694, 6366582] [2] 122880

## Rank

sage: E.rank()

The elliptic curves in class 20181d have rank $$0$$.

## Modular form 20181.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} - q^{4} - 2q^{5} + q^{6} - q^{7} + 3q^{8} + q^{9} + 2q^{10} - 4q^{11} + q^{12} + 2q^{13} + q^{14} + 2q^{15} - q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.