# Properties

 Label 328560.bx Number of curves $6$ Conductor $328560$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("328560.bx1")

sage: E.isogeny_class()

## Elliptic curves in class 328560.bx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
328560.bx1 328560bx4 [0, 1, 0, -7469373976, -248472751706476] [2] 226934784
328560.bx2 328560bx5 [0, 1, 0, -6639650456, 207333307020180] [2] 453869568
328560.bx3 328560bx3 [0, 1, 0, -642335256, -703961563500] [2, 2] 226934784
328560.bx4 328560bx2 [0, 1, 0, -467103256, -3877833640300] [2, 2] 113467392
328560.bx5 328560bx1 [0, 1, 0, -18509336, -105517648236] [2] 56733696 $$\Gamma_0(N)$$-optimal
328560.bx6 328560bx6 [0, 1, 0, 2551267944, -5610613519980] [2] 453869568

## Rank

sage: E.rank()

The elliptic curves in class 328560.bx have rank $$1$$.

## Modular form 328560.2.a.bx

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} - 4q^{11} + 2q^{13} - q^{15} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.