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Properties

Label 4290.g
Number of curves $4$
Conductor $4290$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 4290.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4290.g1 4290f3 \([1, 1, 0, -56162, -5146326]\) \(19591310611933007401/154169730\) \(154169730\) \([2]\) \(10240\) \(1.1622\)  
4290.g2 4290f4 \([1, 1, 0, -4942, -10754]\) \(13352704496588521/7694601378750\) \(7694601378750\) \([2]\) \(10240\) \(1.1622\)  
4290.g3 4290f2 \([1, 1, 0, -3512, -81396]\) \(4792702134385801/13416588900\) \(13416588900\) \([2, 2]\) \(5120\) \(0.81562\)  
4290.g4 4290f1 \([1, 1, 0, -132, -2304]\) \(-257380823881/2035828080\) \(-2035828080\) \([2]\) \(2560\) \(0.46904\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4290.g have rank \(0\).

Complex multiplication

The elliptic curves in class 4290.g do not have complex multiplication.

Modular form 4290.2.a.g

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.