# Properties

 Label 336.b Number of curves 4 Conductor 336 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("336.b1")

sage: E.isogeny_class()

## Elliptic curves in class 336.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
336.b1 336a4 [0, -1, 0, -1828, 30700]  144
336.b2 336a3 [0, -1, 0, -113, 516]  72
336.b3 336a2 [0, -1, 0, -28, 28]  48
336.b4 336a1 [0, -1, 0, 7, 0]  24 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 336.b have rank $$0$$.

## Modular form336.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} + q^{9} + 6q^{11} + 2q^{13} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 