Properties

Label 47190.a
Number of curves $2$
Conductor $47190$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47190.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.a1 47190g2 \([1, 1, 0, -5568, 140958]\) \(10779215329/1232010\) \(2182580867610\) \([2]\) \(122880\) \(1.0999\)  
47190.a2 47190g1 \([1, 1, 0, 482, 11488]\) \(6967871/35100\) \(-62181791100\) \([2]\) \(61440\) \(0.75333\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 47190.a have rank \(1\).

Complex multiplication

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

Modular form 47190.2.a.a

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