Properties

Label 92778.b
Number of curves $2$
Conductor $92778$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 92778.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92778.b1 92778a2 \([1, 1, 0, -84429130, 298562557396]\) \(6174666627902151625/1282563072\) \(13825023526111730688\) \([2]\) \(8478720\) \(3.0595\)  
92778.b2 92778a1 \([1, 1, 0, -5258570, 4697272788]\) \(-1491899855559625/21733834752\) \(-234273684716711313408\) \([2]\) \(4239360\) \(2.7130\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 92778.b have rank \(0\).

Complex multiplication

The elliptic curves in class 92778.b do not have complex multiplication.

Modular form 92778.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.