# Properties

 Label 55470.k Number of curves $2$ Conductor $55470$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("55470.k1")

sage: E.isogeny_class()

## Elliptic curves in class 55470.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55470.k1 55470n2 [1, 0, 1, -2470303, -1494607744]  1064448
55470.k2 55470n1 [1, 0, 1, -159053, -21879244]  532224 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 55470.k have rank $$0$$.

## Modular form 55470.2.a.k

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 2q^{7} - q^{8} + q^{9} - q^{10} + 2q^{11} + q^{12} - 2q^{13} + 2q^{14} + q^{15} + q^{16} + 4q^{17} - q^{18} + 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 