Properties

Label 150.c
Number of curves $4$
Conductor $150$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 150.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
150.c1 150a4 \([1, 0, 0, -828, 9072]\) \(502270291349/1889568\) \(236196000\) \([10]\) \(80\) \(0.46602\)  
150.c2 150a2 \([1, 0, 0, -53, -153]\) \(131872229/18\) \(2250\) \([2]\) \(16\) \(-0.33870\)  
150.c3 150a3 \([1, 0, 0, -28, 272]\) \(-19465109/248832\) \(-31104000\) \([10]\) \(40\) \(0.11945\)  
150.c4 150a1 \([1, 0, 0, -3, -3]\) \(-24389/12\) \(-1500\) \([2]\) \(8\) \(-0.68527\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 150.c do not have complex multiplication.

Modular form 150.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.