Properties

Label 1200.m
Number of curves $4$
Conductor $1200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1200.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.m1 1200q4 \([0, 1, 0, -331208, -73238412]\) \(502270291349/1889568\) \(15116544000000000\) \([2]\) \(9600\) \(1.9639\)  
1200.m2 1200q2 \([0, 1, 0, -21208, 1181588]\) \(131872229/18\) \(144000000000\) \([2]\) \(1920\) \(1.1592\)  
1200.m3 1200q3 \([0, 1, 0, -11208, -2198412]\) \(-19465109/248832\) \(-1990656000000000\) \([2]\) \(4800\) \(1.6173\)  
1200.m4 1200q1 \([0, 1, 0, -1208, 21588]\) \(-24389/12\) \(-96000000000\) \([2]\) \(960\) \(0.81260\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1200.2.a.m

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