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Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 92778.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92778.k1 92778j2 \([1, 0, 1, -4306492, -3945914182]\) \(-370946807737/67765824\) \(-1613591461134443456064\) \([]\) \(5847552\) \(2.7943\)  
92778.k2 92778j1 \([1, 0, 1, 365543, 25315568]\) \(226860023/142884\) \(-3402251883379058724\) \([3]\) \(1949184\) \(2.2449\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 92778.2.a.k

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