Properties

Label 4050.bg
Number of curves $2$
Conductor $4050$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 4050.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4050.bg1 4050be2 \([1, -1, 1, -14555, -675053]\) \(-1642545/8\) \(-1660753125000\) \([]\) \(9720\) \(1.1934\)  
4050.bg2 4050be1 \([1, -1, 1, 445, -5053]\) \(308655/512\) \(-16200000000\) \([3]\) \(3240\) \(0.64408\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4050.bg have rank \(1\).

Complex multiplication

The elliptic curves in class 4050.bg do not have complex multiplication.

Modular form 4050.2.a.bg

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