# Properties

 Label 159120.b Number of curves 4 Conductor 159120 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("159120.b1")

sage: E.isogeny_class()

## Elliptic curves in class 159120.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
159120.b1 159120bd3 [0, 0, 0, -11033283, 14082028738]  8847360
159120.b2 159120bd4 [0, 0, 0, -9247683, -10768074302]  8847360
159120.b3 159120bd2 [0, 0, 0, -924483, 57079618] [2, 2] 4423680
159120.b4 159120bd1 [0, 0, 0, 227517, 7082818]  2211840 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 159120.b have rank $$1$$.

## Modular form 159120.2.a.b

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{7} - 4q^{11} + q^{13} + q^{17} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 