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Properties

Label 52878.g
Number of curves $2$
Conductor $52878$
CM no
Rank $0$
Graph

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

Elliptic curves in class 52878.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52878.g1 52878f2 \([1, 0, 0, -1169746, -38244568738]\) \(-177010260681338006596129/631757862884385194481594\) \(-631757862884385194481594\) \([]\) \(6667920\) \(3.2458\)  
52878.g2 52878f1 \([1, 0, 0, -1127536, 462330752]\) \(-158531287603583609503489/634774607963040384\) \(-634774607963040384\) \([7]\) \(952560\) \(2.2729\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 52878.g have rank \(0\).

Complex multiplication

The elliptic curves in class 52878.g do not have complex multiplication.

Modular form 52878.2.a.g

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