# Properties

 Label 324870bw Number of curves 4 Conductor 324870 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("324870.bw1")

sage: E.isogeny_class()

## Elliptic curves in class 324870bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
324870.bw4 324870bw1 [1, 0, 1, -16294, 55154936] [2] 5898240 $$\Gamma_0(N)$$-optimal
324870.bw3 324870bw2 [1, 0, 1, -2274214, 1303333112] [2, 2] 11796480
324870.bw1 324870bw3 [1, 0, 1, -36260614, 84039825272] [2] 23592960
324870.bw2 324870bw4 [1, 0, 1, -4414534, -1540724104] [2] 23592960

## Rank

sage: E.rank()

The elliptic curves in class 324870bw have rank $$1$$.

## Modular form 324870.2.a.bw

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} + q^{12} + q^{13} - q^{15} + q^{16} + q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.