# Properties

 Label 204624y Number of curves $6$ Conductor $204624$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("204624.bu1")

sage: E.isogeny_class()

## Elliptic curves in class 204624y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
204624.bu5 204624y1 [0, 0, 0, -5532051, -5362105966] [2] 9437184 $$\Gamma_0(N)$$-optimal
204624.bu4 204624y2 [0, 0, 0, -90239331, -329943461470] [2, 2] 18874368
204624.bu3 204624y3 [0, 0, 0, -91968051, -316644418510] [2, 2] 37748736
204624.bu1 204624y4 [0, 0, 0, -1443827091, -21116449256686] [2] 37748736
204624.bu2 204624y5 [0, 0, 0, -299661411, 1623086947874] [2] 75497472
204624.bu6 204624y6 [0, 0, 0, 88065789, -1405237035454] [2] 75497472

## Rank

sage: E.rank()

The elliptic curves in class 204624y have rank $$0$$.

## Modular form 204624.2.a.bu

sage: E.q_eigenform(10)

$$q - 2q^{5} + 4q^{11} + 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.