# Properties

 Label 55545.v Number of curves 4 Conductor 55545 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("55545.v1")

sage: E.isogeny_class()

## Elliptic curves in class 55545.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55545.v1 55545t4 [1, 0, 1, -2271273, -1317693389]  743424
55545.v2 55545t2 [1, 0, 1, -142048, -20569519] [2, 2] 371712
55545.v3 55545t3 [1, 0, 1, -86503, -36810877]  743424
55545.v4 55545t1 [1, 0, 1, -12443, -40087]  185856 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 55545.2.a.v

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels. 