# Properties

 Label 177870.bm Number of curves $2$ Conductor $177870$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("177870.bm1")

sage: E.isogeny_class()

## Elliptic curves in class 177870.bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
177870.bm1 177870hk1 [1, 1, 0, -1817, 10641]  268800 $$\Gamma_0(N)$$-optimal
177870.bm2 177870hk2 [1, 1, 0, 6653, 90259]  537600

## Rank

sage: E.rank()

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

## Modular form 177870.2.a.bm

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. 