# Properties

 Label 177870.cx Number of curves $2$ Conductor $177870$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("177870.cx1")

sage: E.isogeny_class()

## Elliptic curves in class 177870.cx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
177870.cx1 177870gl1 [1, 0, 1, -89059, -3917014] [2] 1881600 $$\Gamma_0(N)$$-optimal
177870.cx2 177870gl2 [1, 0, 1, 325971, -29980898] [2] 3763200

## Rank

sage: E.rank()

The elliptic curves in class 177870.cx have rank $$0$$.

## Modular form 177870.2.a.cx

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} + q^{12} + 2q^{13} - q^{15} + q^{16} - 4q^{17} - q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.