Properties

 Label 219849.u Number of curves $6$ Conductor $219849$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("219849.u1")

sage: E.isogeny_class()

Elliptic curves in class 219849.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
219849.u1 219849p4 [1, 0, 1, -73869272, -244373876341] [2] 10616832
219849.u2 219849p5 [1, 0, 1, -15331317, 18781712509] [2] 21233664
219849.u3 219849p3 [1, 0, 1, -4705282, -3664723825] [2, 2] 10616832
219849.u4 219849p2 [1, 0, 1, -4616837, -3818618125] [2, 2] 5308416
219849.u5 219849p1 [1, 0, 1, -283032, -62075951] [2] 2654208 $$\Gamma_0(N)$$-optimal
219849.u6 219849p6 [1, 0, 1, 4505633, -16261571179] [2] 21233664

Rank

sage: E.rank()

The elliptic curves in class 219849.u have rank $$0$$.

Modular form 219849.2.a.u

sage: E.q_eigenform(10)

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

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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.