# Properties

 Label 55545f Number of curves 4 Conductor 55545 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("55545.c1")

sage: E.isogeny_class()

## Elliptic curves in class 55545f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55545.c3 55545f1 [1, 1, 1, -42860, 3000332] [4] 253440 $$\Gamma_0(N)$$-optimal
55545.c2 55545f2 [1, 1, 1, -172465, -24527770] [2, 2] 506880
55545.c4 55545f3 [1, 1, 1, 253380, -126049218] [2] 1013760
55545.c1 55545f4 [1, 1, 1, -2671990, -1682212750] [2] 1013760

## Rank

sage: E.rank()

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

## Modular form 55545.2.a.c

sage: E.q_eigenform(10)

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

## 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.