Properties

 Label 62866e Number of curves $2$ Conductor $62866$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("62866.e1")

sage: E.isogeny_class()

Elliptic curves in class 62866e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62866.e2 62866e1 [1, -1, 1, -203737, 36268857] [] 455112 $$\Gamma_0(N)$$-optimal
62866.e1 62866e2 [1, -1, 1, -2588947, -4976806507] [] 3185784

Rank

sage: E.rank()

The elliptic curves in class 62866e have rank $$0$$.

Modular form 62866.2.a.e

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} - 3q^{7} + q^{8} - 3q^{9} + q^{10} - 2q^{11} + 2q^{13} - 3q^{14} + q^{16} - q^{17} - 3q^{18} + q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.