Properties

 Label 606.f Number of curves 2 Conductor 606 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("606.f1")
sage: E.isogeny_class()

Elliptic curves in class 606.f

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
606.f1 606f1 [1, 0, 0, -90, 324] 5 100 $$\Gamma_0(N)$$-optimal
606.f2 606f2 [1, 0, 0, 600, -10626] 1 500

Rank

sage: E.rank()

The elliptic curves in class 606.f have rank $$0$$.

Modular form606.2.a.f

sage: E.q_eigenform(10)
$$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 2q^{7} + q^{8} + q^{9} + q^{10} + 2q^{11} + q^{12} + 4q^{13} - 2q^{14} + q^{15} + q^{16} - 2q^{17} + q^{18} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.