# Properties

 Label 55470bb Number of curves $2$ Conductor $55470$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("55470.y1")

sage: E.isogeny_class()

## Elliptic curves in class 55470bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55470.y2 55470bb1 [1, 1, 1, 155, -205] [] 24192 $$\Gamma_0(N)$$-optimal
55470.y1 55470bb2 [1, 1, 1, -1780, 33077] [] 72576

## Rank

sage: E.rank()

The elliptic curves in class 55470bb have rank $$2$$.

## Modular form 55470.2.a.y

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.