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Properties

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

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 92778x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92778.v2 92778x1 \([1, 0, 0, -59689, 6302153]\) \(-2181825073/331632\) \(-3574732737986928\) \([2]\) \(847872\) \(1.7137\) \(\Gamma_0(N)\)-optimal
92778.v1 92778x2 \([1, 0, 0, -987469, 377599709]\) \(9878863930993/185556\) \(2000148079587924\) \([2]\) \(1695744\) \(2.0603\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 92778.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 2 q^{5} + q^{6} - q^{7} + q^{8} + q^{9} - 2 q^{10} - 6 q^{11} + q^{12} + 4 q^{13} - q^{14} - 2 q^{15} + q^{16} + 6 q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.