Properties

Label 150.a
Number of curves 4
Conductor 150
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("150.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 150.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
150.a1 150b4 [1, 1, 0, -20700, 1134000] [2] 400  
150.a2 150b2 [1, 1, 0, -1325, -19125] [2] 80  
150.a3 150b3 [1, 1, 0, -700, 34000] [2] 200  
150.a4 150b1 [1, 1, 0, -75, -375] [2] 40 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 150.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{6} + 2q^{7} - q^{8} + q^{9} + 2q^{11} - q^{12} + 6q^{13} - 2q^{14} + q^{16} + 2q^{17} - q^{18} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.