# Properties

 Label 1666.m Number of curves $4$ Conductor $1666$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 1666.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1666.m1 1666l4 [1, 1, 1, -5538, 107309] [2] 3456
1666.m2 1666l3 [1, 1, 1, -5048, 135925] [2] 1728
1666.m3 1666l2 [1, 1, 1, -2108, -38123] [2] 1152
1666.m4 1666l1 [1, 1, 1, -148, -491] [2] 576 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1666.m have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1666.m do not have complex multiplication.

## Modular form1666.2.a.m

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.