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Properties

Label 191634.n
Number of curves $4$
Conductor $191634$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 191634.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
191634.n1 191634j3 \([1, 1, 1, -719503, -235205455]\) \(8671983378625/82308\) \(390971579868228\) \([2]\) \(2488320\) \(1.9623\)  
191634.n2 191634j4 \([1, 1, 1, -702693, -246696771]\) \(-8078253774625/846825858\) \(-4022511099474263778\) \([2]\) \(4976640\) \(2.3089\)  
191634.n3 191634j1 \([1, 1, 1, -13483, 40409]\) \(57066625/32832\) \(155955422440512\) \([2]\) \(829440\) \(1.4130\) \(\Gamma_0(N)\)-optimal
191634.n4 191634j2 \([1, 1, 1, 53757, 390057]\) \(3616805375/2105352\) \(-10000641463997832\) \([2]\) \(1658880\) \(1.7596\)  

Rank

sage: E.rank()
 

The elliptic curves in class 191634.n have rank \(0\).

Complex multiplication

The elliptic curves in class 191634.n do not have complex multiplication.

Modular form 191634.2.a.n

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.