Properties

 Label 22386bc Number of curves 2 Conductor 22386 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22386.u1")

sage: E.isogeny_class()

Elliptic curves in class 22386bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22386.u2 22386bc1 [1, 0, 0, -307482, 41491044] [3] 435456 $$\Gamma_0(N)$$-optimal
22386.u1 22386bc2 [1, 0, 0, -10303962, -12729674844] [] 1306368

Rank

sage: E.rank()

The elliptic curves in class 22386bc have rank $$1$$.

Modular form 22386.2.a.u

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - 3q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - 3q^{10} - 3q^{11} + q^{12} + q^{13} + q^{14} - 3q^{15} + q^{16} + 3q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.