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Properties

Label 92778.e
Number of curves $2$
Conductor $92778$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 92778.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92778.e1 92778e2 \([1, 0, 1, -1517838186, -22760780751308]\) \(345556776695240375/1458274104\) \(1631998987923033646845768\) \([2]\) \(46780416\) \(3.8544\)  
92778.e2 92778e1 \([1, 0, 1, -93386626, -367262666860]\) \(-80481680984375/5489031744\) \(-6142942692538826237235648\) \([2]\) \(23390208\) \(3.5078\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 92778.e have rank \(1\).

Complex multiplication

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

Modular form 92778.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.