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Properties

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

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 92778.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92778.i1 92778g2 \([1, 0, 1, -631189766, -6104034509344]\) \(-1167940433374113625/78447412008\) \(-1867933815195760105826088\) \([]\) \(43856640\) \(3.7125\)  
92778.i2 92778g1 \([1, 0, 1, -465041, -23293122586]\) \(-467103625/9843350202\) \(-234382833371925045025722\) \([3]\) \(14618880\) \(3.1632\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 92778.2.a.i

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.