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Properties

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

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Show commands: SageMath
E = EllipticCurve("bh1")
 
E.isogeny_class()
 

Elliptic curves in class 47190.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.bh1 47190bj1 \([1, 0, 1, -10288, 925406]\) \(-561712921/1404000\) \(-300959868924000\) \([3]\) \(190080\) \(1.4661\) \(\Gamma_0(N)\)-optimal
47190.bh2 47190bj2 \([1, 0, 1, 89537, -20716654]\) \(370336757879/1079869440\) \(-231479604784496640\) \([]\) \(570240\) \(2.0154\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 47190.2.a.bh

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