# Properties

 Label 1008k Number of curves 6 Conductor 1008 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1008.l1")
sage: E.isogeny_class()

## Elliptic curves in class 1008k

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1008.l6 1008k1 [0, 0, 0, 141, -142] 2 256 $$\Gamma_0(N)$$-optimal
1008.l5 1008k2 [0, 0, 0, -579, -1150] 4 512
1008.l2 1008k3 [0, 0, 0, -7059, -227950] 4 1024
1008.l3 1008k4 [0, 0, 0, -5619, 161138] 2 1024
1008.l1 1008k5 [0, 0, 0, -112899, -14601022] 2 2048
1008.l4 1008k6 [0, 0, 0, -4899, -370078] 4 2048

## Rank

sage: E.rank()

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

## Modular form1008.2.a.l

sage: E.q_eigenform(10)
$$q + 2q^{5} + q^{7} + 4q^{11} - 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.