Properties

Label 1200.o
Number of curves $6$
Conductor $1200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1200.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1200.o1 1200e5 [0, 1, 0, -80008, 8683988] [2] 3072  
1200.o2 1200e3 [0, 1, 0, -5008, 133988] [2, 2] 1536  
1200.o3 1200e6 [0, 1, 0, -2008, 295988] [2] 3072  
1200.o4 1200e2 [0, 1, 0, -508, -1012] [2, 2] 768  
1200.o5 1200e1 [0, 1, 0, -383, -3012] [2] 384 \(\Gamma_0(N)\)-optimal
1200.o6 1200e4 [0, 1, 0, 1992, -6012] [4] 1536  

Rank

sage: E.rank()
 

The elliptic curves in class 1200.o have rank \(0\).

Complex multiplication

The elliptic curves in class 1200.o do not have complex multiplication.

Modular form 1200.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} + 4q^{11} - 6q^{13} + 6q^{17} + 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.