# Properties

 Label 5184.y Number of curves $2$ Conductor $5184$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5184.y1")

sage: E.isogeny_class()

## Elliptic curves in class 5184.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5184.y1 5184j1 [0, 0, 0, -396, 3312] [] 2304 $$\Gamma_0(N)$$-optimal
5184.y2 5184j2 [0, 0, 0, 2484, -4752] [] 6912

## Rank

sage: E.rank()

The elliptic curves in class 5184.y have rank $$1$$.

## Modular form5184.2.a.y

sage: E.q_eigenform(10)

$$q + 3q^{5} - 4q^{7} + q^{13} - 3q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 