Properties

 Label 366.f Number of curves 2 Conductor 366 CM no Rank 0 Graph Related objects

Show commands for: SageMath
sage: E = EllipticCurve("366.f1")
sage: E.isogeny_class()

Elliptic curves in class 366.f

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
366.f1 366b2 [1, 0, 0, -515, -5697] 1 300
366.f2 366b1 [1, 0, 0, -5, 33] 5 60 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 366.f have rank $$0$$.

Modular form366.2.a.f

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

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. 