Properties

 Label 1006b Number of curves 2 Conductor 1006 CM no Rank 0 Graph Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1006.a1")
sage: E.isogeny_class()

Elliptic curves in class 1006b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1006.a2 1006b1 [1, -1, 0, 8, 0] 2 63 $$\Gamma_0(N)$$-optimal
1006.a1 1006b2 [1, -1, 0, -32, 24] 2 126

Rank

sage: E.rank()

The elliptic curves in class 1006b have rank $$0$$.

Modular form1006.2.a.a

sage: E.q_eigenform(10)
$$q - q^{2} + q^{4} - q^{8} - 3q^{9} + 4q^{11} + 2q^{13} + q^{16} - 2q^{17} + 3q^{18} - 2q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels. 