# Properties

 Label 55473l Number of curves 4 Conductor 55473 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("55473.n1")

sage: E.isogeny_class()

## Elliptic curves in class 55473l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55473.n3 55473l1 [1, 0, 1, -10962, -438929] [2] 105600 $$\Gamma_0(N)$$-optimal
55473.n2 55473l2 [1, 0, 1, -19367, 324245] [2, 2] 211200
55473.n4 55473l3 [1, 0, 1, 73088, 2543165] [2] 422400
55473.n1 55473l4 [1, 0, 1, -246302, 46982081] [2] 422400

## Rank

sage: E.rank()

The elliptic curves in class 55473l have rank $$0$$.

## Modular form 55473.2.a.n

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.