# Properties

 Label 338130.bu Number of curves 2 Conductor 338130 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("338130.bu1")

sage: E.isogeny_class()

## Elliptic curves in class 338130.bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
338130.bu1 338130bu1 [1, -1, 0, -35425674, -80222737932]  35389440 $$\Gamma_0(N)$$-optimal
338130.bu2 338130bu2 [1, -1, 0, -5462154, -211624758540]  70778880

## Rank

sage: E.rank()

The elliptic curves in class 338130.bu have rank $$1$$.

## Modular form 338130.2.a.bu

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} + 2q^{7} - q^{8} - q^{10} - q^{13} - 2q^{14} + q^{16} + 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 