# Properties

 Label 55545q Number of curves 2 Conductor 55545 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("55545.q1")

sage: E.isogeny_class()

## Elliptic curves in class 55545q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55545.q1 55545q1 [0, 1, 1, -3235, -71921] [] 31104 $$\Gamma_0(N)$$-optimal
55545.q2 55545q2 [0, 1, 1, 905, -235244] [] 93312

## Rank

sage: E.rank()

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

## Modular form 55545.2.a.q

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{4} + q^{5} - q^{7} + q^{9} - 2q^{12} - q^{13} + q^{15} + 4q^{16} - 3q^{17} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 