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Properties

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

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Show commands: SageMath
E = EllipticCurve("db1")
 
E.isogeny_class()
 

Elliptic curves in class 47190.db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.db1 47190db2 \([1, 0, 0, -346970, -78551538]\) \(2607614922465721/5488604550\) \(9723397765202550\) \([2]\) \(614400\) \(1.9528\)  
47190.db2 47190db1 \([1, 0, 0, -14220, -2085588]\) \(-179501589721/955597500\) \(-1692899262697500\) \([2]\) \(307200\) \(1.6063\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 47190.2.a.db

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