# Properties

 Label 106a Number of curves 2 Conductor 106 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("106.c1")
sage: E.isogeny_class()

## Elliptic curves in class 106a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
106.c2 106a1 [1, 0, 0, 1, 1] 3 6 $$\Gamma_0(N)$$-optimal
106.c1 106a2 [1, 0, 0, -9, -29] 1 18

## Rank

sage: E.rank()

The elliptic curves in class 106a have rank $$0$$.

## Modular form106.2.a.c

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 