# Properties

 Label 35574.bu Number of curves 4 Conductor 35574 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35574.bu1")

sage: E.isogeny_class()

## Elliptic curves in class 35574.bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35574.bu1 35574by3 [1, 1, 1, -477408, -126677055] [2] 518400
35574.bu2 35574by4 [1, 1, 1, -240248, -252276991] [2] 1036800
35574.bu3 35574by1 [1, 1, 1, -32733, 2136399] [2] 172800 $$\Gamma_0(N)$$-optimal
35574.bu4 35574by2 [1, 1, 1, 26557, 9085187] [2] 345600

## Rank

sage: E.rank()

The elliptic curves in class 35574.bu have rank $$0$$.

## Modular form 35574.2.a.bu

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.