Properties

Label 76050.bs
Number of curves $6$
Conductor $76050$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("76050.bs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 76050.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76050.bs1 76050bc6 [1, -1, 0, -342796167, 2442964936491] [2] 16515072  
76050.bs2 76050bc4 [1, -1, 0, -32131917, -70042290759] [2] 8257536  
76050.bs3 76050bc3 [1, -1, 0, -21484917, 37950230241] [2, 2] 8257536  
76050.bs4 76050bc5 [1, -1, 0, -4373667, 96727373991] [2] 16515072  
76050.bs5 76050bc2 [1, -1, 0, -2472417, -550082259] [2, 2] 4128768  
76050.bs6 76050bc1 [1, -1, 0, 569583, -66404259] [2] 2064384 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 76050.bs have rank \(0\).

Modular form 76050.2.a.bs

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{8} + 4q^{11} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.