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Properties

Label 8034.g
Number of curves $4$
Conductor $8034$
CM no
Rank $0$
Graph

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

Elliptic curves in class 8034.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8034.g1 8034k3 \([1, 0, 0, -2229, 40293]\) \(1224802586728657/953137692\) \(953137692\) \([4]\) \(9984\) \(0.65427\)  
8034.g2 8034k2 \([1, 0, 0, -169, 329]\) \(534003898897/258180624\) \(258180624\) \([2, 2]\) \(4992\) \(0.30770\)  
8034.g3 8034k1 \([1, 0, 0, -89, -327]\) \(78018694417/1028352\) \(1028352\) \([2]\) \(2496\) \(-0.038873\) \(\Gamma_0(N)\)-optimal
8034.g4 8034k4 \([1, 0, 0, 611, 2669]\) \(25223358788783/17557937436\) \(-17557937436\) \([2]\) \(9984\) \(0.65427\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8034.g have rank \(0\).

Complex multiplication

The elliptic curves in class 8034.g do not have complex multiplication.

Modular form 8034.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.