Properties

Label 150.b
Number of curves 8
Conductor 150
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("150.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 150.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
150.b1 150c7 [1, 1, 1, -133338, -18795969] [2] 576  
150.b2 150c8 [1, 1, 1, -11338, -67969] [2] 576  
150.b3 150c6 [1, 1, 1, -8338, -295969] [2, 2] 288  
150.b4 150c5 [1, 1, 1, -7213, 232781] [2] 192  
150.b5 150c4 [1, 1, 1, -1713, -24219] [2] 192  
150.b6 150c2 [1, 1, 1, -463, 3281] [2, 2] 96  
150.b7 150c3 [1, 1, 1, -338, -7969] [4] 144  
150.b8 150c1 [1, 1, 1, 37, 281] [4] 48 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 150.b have rank \(0\).

Modular form 150.2.a.b

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.