# Properties

 Label 170.a Number of curves 4 Conductor 170 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("170.a1")
sage: E.isogeny_class()

## Elliptic curves in class 170.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
170.a1 170b3 [1, 0, 1, -4169, -20724] 2 480
170.a2 170b1 [1, 0, 1, -2554, 49452] 6 160 $$\Gamma_0(N)$$-optimal
170.a3 170b2 [1, 0, 1, -2474, 52716] 6 320
170.a4 170b4 [1, 0, 1, 16311, -159988] 2 960

## Rank

sage: E.rank()

The elliptic curves in class 170.a have rank $$0$$.

## Modular form170.2.a.a

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.