Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1200e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.o5 1200e1 \([0, 1, 0, -383, -3012]\) \(24918016/45\) \(11250000\) \([2]\) \(384\) \(0.24500\) \(\Gamma_0(N)\)-optimal
1200.o4 1200e2 \([0, 1, 0, -508, -1012]\) \(3631696/2025\) \(8100000000\) \([2, 2]\) \(768\) \(0.59157\)  
1200.o2 1200e3 \([0, 1, 0, -5008, 133988]\) \(868327204/5625\) \(90000000000\) \([2, 2]\) \(1536\) \(0.93814\)  
1200.o6 1200e4 \([0, 1, 0, 1992, -6012]\) \(54607676/32805\) \(-524880000000\) \([4]\) \(1536\) \(0.93814\)  
1200.o1 1200e5 \([0, 1, 0, -80008, 8683988]\) \(1770025017602/75\) \(2400000000\) \([2]\) \(3072\) \(1.2847\)  
1200.o3 1200e6 \([0, 1, 0, -2008, 295988]\) \(-27995042/1171875\) \(-37500000000000\) \([2]\) \(3072\) \(1.2847\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1200.2.a.e

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.