# Properties

 Label 55470m Number of curves $2$ Conductor $55470$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("55470.j1")

sage: E.isogeny_class()

## Elliptic curves in class 55470m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55470.j2 55470m1 [1, 0, 1, -66260803, -207555750802] [2] 7265280 $$\Gamma_0(N)$$-optimal
55470.j1 55470m2 [1, 0, 1, -1060098303, -13285264645802] [2] 14530560

## Rank

sage: E.rank()

The elliptic curves in class 55470m have rank $$1$$.

## Modular form 55470.2.a.j

sage: E.q_eigenform(10)

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

## 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.