# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("55470.o1")

sage: E.isogeny_class()

## Elliptic curves in class 55470o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55470.o2 55470o1 [1, 0, 1, -18963383, 32958641306]  9313920 $$\Gamma_0(N)$$-optimal
55470.o1 55470o2 [1, 0, 1, -306519863, 2065522864538]  18627840

## Rank

sage: E.rank()

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

## Modular form 55470.2.a.o

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 