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Properties

Label 158634.g
Number of curves $2$
Conductor $158634$
CM no
Rank $0$
Graph

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

Elliptic curves in class 158634.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158634.g1 158634p2 \([1, -1, 0, -10527714, 1032603355926]\) \(-177010260681338006596129/631757862884385194481594\) \(-460551482042716806777082026\) \([]\) \(53343360\) \(3.7951\)  
158634.g2 158634p1 \([1, -1, 0, -10147824, -12482930304]\) \(-158531287603583609503489/634774607963040384\) \(-462750689205056439936\) \([]\) \(7620480\) \(2.8222\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 158634.g have rank \(0\).

Complex multiplication

The elliptic curves in class 158634.g do not have complex multiplication.

Modular form 158634.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} + 2 q^{11} - q^{14} + q^{16} - 4 q^{17} - q^{19} + O(q^{20})\) 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.