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Properties

Label 22386.u
Number of curves $2$
Conductor $22386$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 22386.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22386.u1 22386bc2 \([1, 0, 0, -10303962, -12729674844]\) \(120986373702456846135875233/21429653098766238144\) \(21429653098766238144\) \([]\) \(1306368\) \(2.7140\)  
22386.u2 22386bc1 \([1, 0, 0, -307482, 41491044]\) \(3215014175651328584353/1115930860975816704\) \(1115930860975816704\) \([3]\) \(435456\) \(2.1646\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 22386.u have rank \(1\).

Complex multiplication

The elliptic curves in class 22386.u do not have complex multiplication.

Modular form 22386.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 3 q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - 3 q^{10} - 3 q^{11} + q^{12} + q^{13} + q^{14} - 3 q^{15} + q^{16} + 3 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.