# Properties

 Label 166635.n Number of curves 4 Conductor 166635 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("166635.n1")

sage: E.isogeny_class()

## Elliptic curves in class 166635.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
166635.n1 166635n4 [1, -1, 1, -535712, -150774514] [2] 1441792
166635.n2 166635n2 [1, -1, 1, -35807, -2002786] [2, 2] 720896
166635.n3 166635n1 [1, -1, 1, -12002, 482456] [2] 360448 $$\Gamma_0(N)$$-optimal
166635.n4 166635n3 [1, -1, 1, 83218, -12572206] [2] 1441792

## Rank

sage: E.rank()

The elliptic curves in class 166635.n have rank $$0$$.

## Modular form 166635.2.a.n

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + q^{5} - q^{7} + 3q^{8} - q^{10} - 6q^{13} + q^{14} - q^{16} + 2q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.