# Properties

 Label 159120bx Number of curves 2 Conductor 159120 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("159120.bp1")

sage: E.isogeny_class()

## Elliptic curves in class 159120bx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
159120.bp1 159120bx1 [0, 0, 0, -1961283, 1045150018]  2949120 $$\Gamma_0(N)$$-optimal
159120.bp2 159120bx2 [0, 0, 0, -302403, 2756782402]  5898240

## Rank

sage: E.rank()

The elliptic curves in class 159120bx have rank $$0$$.

## Modular form 159120.2.a.bp

sage: E.q_eigenform(10)

$$q - q^{5} + 2q^{7} - q^{13} + q^{17} - 2q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 