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Properties

Label 43706.x
Number of curves $2$
Conductor $43706$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 43706.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43706.x1 43706v2 \([1, -1, 1, -357528, -90190667]\) \(-1064019559329/125497034\) \(-596123993436321194\) \([]\) \(987840\) \(2.1466\)  
43706.x2 43706v1 \([1, -1, 1, -4518, 179893]\) \(-2146689/1664\) \(-7904173457024\) \([]\) \(141120\) \(1.1736\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 43706.x have rank \(1\).

Complex multiplication

The elliptic curves in class 43706.x do not have complex multiplication.

Modular form 43706.2.a.x

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.