Properties

Label 157794x
Number of curves $4$
Conductor $157794$
CM no
Rank $0$
Graph

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

Elliptic curves in class 157794x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
157794.bq3 157794x1 \([1, 1, 1, -2029, -32365]\) \(38272753/4368\) \(105432901392\) \([2]\) \(221184\) \(0.84743\) \(\Gamma_0(N)\)-optimal
157794.bq2 157794x2 \([1, 1, 1, -7809, 228891]\) \(2181825073/298116\) \(7195795520004\) \([2, 2]\) \(442368\) \(1.1940\)  
157794.bq1 157794x3 \([1, 1, 1, -120519, 16053375]\) \(8020417344913/187278\) \(4520435647182\) \([2]\) \(884736\) \(1.5406\)  
157794.bq4 157794x4 \([1, 1, 1, 12421, 1240391]\) \(8780064047/32388174\) \(-781771784709006\) \([2]\) \(884736\) \(1.5406\)  

Rank

sage: E.rank()
 

The elliptic curves in class 157794x have rank \(0\).

Complex multiplication

The elliptic curves in class 157794x do not have complex multiplication.

Modular form 157794.2.a.x

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.