Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1200.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.r1 1200g4 \([0, 1, 0, -5408, 151188]\) \(546718898/405\) \(12960000000\) \([4]\) \(1536\) \(0.87412\)  
1200.r2 1200g3 \([0, 1, 0, -3408, -76812]\) \(136835858/1875\) \(60000000000\) \([2]\) \(1536\) \(0.87412\)  
1200.r3 1200g2 \([0, 1, 0, -408, 1188]\) \(470596/225\) \(3600000000\) \([2, 2]\) \(768\) \(0.52755\)  
1200.r4 1200g1 \([0, 1, 0, 92, 188]\) \(21296/15\) \(-60000000\) \([2]\) \(384\) \(0.18097\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1200.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{3} + 4q^{7} + q^{9} + 6q^{13} + 2q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.