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Properties

Label 162922f
Number of curves $2$
Conductor $162922$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 162922f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162922.b2 162922f1 \([1, 0, 1, 13986, 1058640]\) \(13651919/29696\) \(-658192868086784\) \([]\) \(581360\) \(1.5276\) \(\Gamma_0(N)\)-optimal
162922.b1 162922f2 \([1, 0, 1, -1278154, -560067200]\) \(-10418796526321/82044596\) \(-1818466054426908884\) \([]\) \(2906800\) \(2.3323\)  

Rank

sage: E.rank()
 

The elliptic curves in class 162922f have rank \(1\).

Complex multiplication

The elliptic curves in class 162922f do not have complex multiplication.

Modular form 162922.2.a.f

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.