# Properties

 Label 126.b Number of curves 6 Conductor 126 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("126.b1")
sage: E.isogeny_class()

## Elliptic curves in class 126.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
126.b1 126a6 [1, -1, 1, -24575, 1488935] 6 144
126.b2 126a5 [1, -1, 1, -1535, 23591] 6 72
126.b3 126a4 [1, -1, 1, -320, 1883] 6 48
126.b4 126a2 [1, -1, 1, -95, -331] 2 16
126.b5 126a1 [1, -1, 1, -5, -7] 2 8 $$\Gamma_0(N)$$-optimal
126.b6 126a3 [1, -1, 1, 40, 155] 6 24

## Rank

sage: E.rank()

The elliptic curves in class 126.b have rank $$0$$.

## Modular form126.2.a.b

sage: E.q_eigenform(10)
$$q + q^{2} + q^{4} + q^{7} + q^{8} - 4q^{13} + q^{14} + q^{16} - 6q^{17} + 2q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.