# Properties

 Label 168.b Number of curves $4$ Conductor $168$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 168.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
168.b1 168a3 [0, 1, 0, -152, 672]  32
168.b2 168a2 [0, 1, 0, -12, 0] [2, 2] 16
168.b3 168a1 [0, 1, 0, -7, -10]  8 $$\Gamma_0(N)$$-optimal
168.b4 168a4 [0, 1, 0, 48, 48]  32

## Rank

sage: E.rank()

The elliptic curves in class 168.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 168.b do not have complex multiplication.

## Modular form168.2.a.b

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{5} - q^{7} + q^{9} - 2q^{13} + 2q^{15} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 