# Properties

 Label 156.b Number of curves $4$ Conductor $156$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 156.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
156.b1 156b4 [0, 1, 0, -748, -7564]  72
156.b2 156b3 [0, 1, 0, -733, -7888]  36
156.b3 156b2 [0, 1, 0, -148, 644]  24
156.b4 156b1 [0, 1, 0, -13, -4]  12 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 156.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 156.b do not have complex multiplication.

## Modular form156.2.a.b

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{7} + q^{9} + q^{13} - 6q^{17} + 2q^{19} + O(q^{20})$$

## 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 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. 