# Properties

 Label 158.b Number of curves 3 Conductor 158 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("158.b1")

sage: E.isogeny_class()

## Elliptic curves in class 158.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
158.b1 158d2 [1, 0, 1, -5217, -145452] [] 120
158.b2 158d1 [1, 0, 1, -82, -92]  40 $$\Gamma_0(N)$$-optimal
158.b3 158d3 [1, 0, 1, -47, 118]  120

## Rank

sage: E.rank()

The elliptic curves in class 158.b have rank $$0$$.

## Modular form158.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + 3q^{5} - q^{6} - q^{7} - q^{8} - 2q^{9} - 3q^{10} + q^{12} + 5q^{13} + q^{14} + 3q^{15} + q^{16} + 2q^{18} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 