# Properties

 Label 57330.bu Number of curves $6$ Conductor $57330$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("57330.bu1")

sage: E.isogeny_class()

## Elliptic curves in class 57330.bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
57330.bu1 57330cm6 [1, -1, 0, -3975624, -3050103330] [2] 1572864
57330.bu2 57330cm4 [1, -1, 0, -372654, 87584328] [2] 786432
57330.bu3 57330cm3 [1, -1, 0, -249174, -47329920] [2, 2] 786432
57330.bu4 57330cm5 [1, -1, 0, -50724, -120796110] [2] 1572864
57330.bu5 57330cm2 [1, -1, 0, -28674, 694980] [2, 2] 393216
57330.bu6 57330cm1 [1, -1, 0, 6606, 81108] [2] 196608 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 57330.bu have rank $$2$$.

## Modular form 57330.2.a.bu

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 4q^{11} - q^{13} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.