# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("126.a1")

sage: E.isogeny_class()

## Elliptic curves in class 126.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
126.a1 126b3 [1, -1, 0, -12096, -509036] [2] 128
126.a2 126b5 [1, -1, 0, -8226, 286474] [2] 256
126.a3 126b4 [1, -1, 0, -936, -3668] [2, 2] 128
126.a4 126b2 [1, -1, 0, -756, -7808] [2, 2] 64
126.a5 126b1 [1, -1, 0, -36, -176] [2] 32 $$\Gamma_0(N)$$-optimal
126.a6 126b6 [1, -1, 0, 3474, -31010] [2] 256

## Rank

sage: E.rank()

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

## Modular form126.2.a.a

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.