# Properties

 Label 1008e Number of curves 4 Conductor 1008 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1008.b1")

sage: E.isogeny_class()

## Elliptic curves in class 1008e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1008.b4 1008e1 [0, 0, 0, -66, 1339]  384 $$\Gamma_0(N)$$-optimal
1008.b3 1008e2 [0, 0, 0, -2271, 41470] [2, 2] 768
1008.b2 1008e3 [0, 0, 0, -3531, -9686]  1536
1008.b1 1008e4 [0, 0, 0, -36291, 2661010]  1536

## Rank

sage: E.rank()

The elliptic curves in class 1008e have rank $$0$$.

## Modular form1008.2.a.b

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 