# Properties

 Label 184590q Number of curves 2 Conductor 184590 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("184590.f1")

sage: E.isogeny_class()

## Elliptic curves in class 184590q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
184590.f2 184590q1 [1, -1, 0, 86295, -63082675] [] 5531904 $$\Gamma_0(N)$$-optimal
184590.f1 184590q2 [1, -1, 0, -49913655, 135823538195] [] 38723328

## Rank

sage: E.rank()

The elliptic curves in class 184590q have rank $$0$$.

## Modular form 184590.2.a.f

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.