# Properties

 Label 53235.bg Number of curves 4 Conductor 53235 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("53235.bg1")

sage: E.isogeny_class()

## Elliptic curves in class 53235.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53235.bg1 53235bc4 [1, -1, 0, -171144, 27292383] [2] 245760
53235.bg2 53235bc2 [1, -1, 0, -11439, 366120] [2, 2] 122880
53235.bg3 53235bc1 [1, -1, 0, -3834, -85617] [2] 61440 $$\Gamma_0(N)$$-optimal
53235.bg4 53235bc3 [1, -1, 0, 26586, 2259765] [2] 245760

## Rank

sage: E.rank()

The elliptic curves in class 53235.bg have rank $$1$$.

## Modular form 53235.2.a.bg

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + q^{5} - q^{7} - 3q^{8} + q^{10} - q^{14} - q^{16} - 2q^{17} + 8q^{19} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels.