Properties

 Label 550.j Number of curves 3 Conductor 550 CM no Rank 0 Graph Related objects

Show commands for: SageMath
sage: E = EllipticCurve("550.j1")
sage: E.isogeny_class()

Elliptic curves in class 550.j

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
550.j1 550k3 [1, 1, 1, -30328, 2020281] 5 1200
550.j2 550k1 [1, 1, 1, -28, -69] 1 48 $$\Gamma_0(N)$$-optimal
550.j3 550k2 [1, 1, 1, 197, 681] 5 240

Rank

sage: E.rank()

The elliptic curves in class 550.j have rank $$0$$.

Modular form550.2.a.j

sage: E.q_eigenform(10)
$$q + q^{2} - q^{3} + q^{4} - q^{6} + 3q^{7} + q^{8} - 2q^{9} + q^{11} - q^{12} + 4q^{13} + 3q^{14} + q^{16} + 3q^{17} - 2q^{18} - 5q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrr} 1 & 25 & 5 \\ 25 & 1 & 5 \\ 5 & 5 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels. 