Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("150.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 150.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
150.c1 150a4 [1, 0, 0, -828, 9072] [10] 80  
150.c2 150a2 [1, 0, 0, -53, -153] [2] 16  
150.c3 150a3 [1, 0, 0, -28, 272] [10] 40  
150.c4 150a1 [1, 0, 0, -3, -3] [2] 8 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 150.2.a.c

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.