Properties

 Label 3006e Number of curves 2 Conductor 3006 CM no Rank 1 Graph Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3006.d1")
sage: E.isogeny_class()

Elliptic curves in class 3006e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
3006.d2 3006e1 [1, -1, 1, -41, 425] 2 1152 $$\Gamma_0(N)$$-optimal
3006.d1 3006e2 [1, -1, 1, -1121, 14681] 2 2304

Rank

sage: E.rank()

The elliptic curves in class 3006e have rank $$1$$.

Modular form3006.2.a.d

sage: E.q_eigenform(10)
$$q + q^{2} + q^{4} - 2q^{5} - 4q^{7} + q^{8} - 2q^{10} + 4q^{11} - 4q^{14} + q^{16} + 4q^{17} - 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels. 