Properties

 Label 1008.b 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 1008.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1008.b1 1008e4 [0, 0, 0, -36291, 2661010] 4 1536
1008.b2 1008e3 [0, 0, 0, -3531, -9686] 2 1536
1008.b3 1008e2 [0, 0, 0, -2271, 41470] 4 768
1008.b4 1008e1 [0, 0, 0, -66, 1339] 2 384 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 1008.b 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 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. 