# Properties

 Label 264.b Number of curves 4 Conductor 264 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("264.b1")

sage: E.isogeny_class()

## Elliptic curves in class 264.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
264.b1 264c4 [0, 1, 0, -704, 6960]  96
264.b2 264c3 [0, 1, 0, -104, -288]  96
264.b3 264c2 [0, 1, 0, -44, 96] [2, 2] 48
264.b4 264c1 [0, 1, 0, 1, 6]  24 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 264.b have rank $$0$$.

## Modular form264.2.a.b

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} + 4q^{7} + q^{9} - q^{11} + 6q^{13} - 2q^{15} + 6q^{17} - 8q^{19} + O(q^{20})$$

## 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. 