# Properties

 Label 55545l Number of curves 2 Conductor 55545 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("55545.u1")

sage: E.isogeny_class()

## Elliptic curves in class 55545l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55545.u1 55545l1 [1, 0, 1, -760449, 254433247] [2] 608256 $$\Gamma_0(N)$$-optimal
55545.u2 55545l2 [1, 0, 1, -429824, 477142247] [2] 1216512

## Rank

sage: E.rank()

The elliptic curves in class 55545l have rank $$0$$.

## Modular form 55545.2.a.u

sage: E.q_eigenform(10)

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

## 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.