# Properties

 Label 54208be Number of curves $4$ Conductor $54208$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("be1")

sage: E.isogeny_class()

## Elliptic curves in class 54208be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54208.bl4 54208be1 [0, 0, 0, 484, -21296]  40960 $$\Gamma_0(N)$$-optimal
54208.bl3 54208be2 [0, 0, 0, -9196, -319440] [2, 2] 81920
54208.bl2 54208be3 [0, 0, 0, -28556, 1469424]  163840
54208.bl1 54208be4 [0, 0, 0, -144716, -21189520]  163840

## Rank

sage: E.rank()

The elliptic curves in class 54208be have rank $$1$$.

## Complex multiplication

The elliptic curves in class 54208be do not have complex multiplication.

## Modular form 54208.2.a.be

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} - 3q^{9} + 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 