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Properties

Label 47190.cn
Number of curves $2$
Conductor $47190$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cn1")
 
E.isogeny_class()
 

Elliptic curves in class 47190.cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.cn1 47190cj2 \([1, 0, 0, -66796661, 210121547241]\) \(-18605093748570727251049/91759078125000\) \(-162556804202203125000\) \([]\) \(5443200\) \(3.0776\)  
47190.cn2 47190cj1 \([1, 0, 0, -492896, 521761890]\) \(-7475384530020889/62069784455250\) \(-109960409419327145250\) \([]\) \(1814400\) \(2.5283\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 47190.cn have rank \(0\).

Complex multiplication

The elliptic curves in class 47190.cn do not have complex multiplication.

Modular form 47190.2.a.cn

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