Properties

 Label 1005b Number of curves 2 Conductor 1005 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1005.a1")
sage: E.isogeny_class()

Elliptic curves in class 1005b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1005.a2 1005b1 [0, 1, 1, 239, 295] 3 480 $$\Gamma_0(N)$$-optimal
1005.a1 1005b2 [0, 1, 1, -3001, -70904] 1 1440

Rank

sage: E.rank()

The elliptic curves in class 1005b have rank $$1$$.

Modular form1005.2.a.a

sage: E.q_eigenform(10)
$$q + q^{3} - 2q^{4} - q^{5} + 2q^{7} + q^{9} - 6q^{11} - 2q^{12} + 2q^{13} - q^{15} + 4q^{16} - 3q^{17} - q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.