Properties

Label 600.a
Number of curves $4$
Conductor $600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 600.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
600.a1 600f3 \([0, -1, 0, -5408, -151188]\) \(546718898/405\) \(12960000000\) \([2]\) \(768\) \(0.87412\)  
600.a2 600f4 \([0, -1, 0, -3408, 76812]\) \(136835858/1875\) \(60000000000\) \([2]\) \(768\) \(0.87412\)  
600.a3 600f2 \([0, -1, 0, -408, -1188]\) \(470596/225\) \(3600000000\) \([2, 2]\) \(384\) \(0.52755\)  
600.a4 600f1 \([0, -1, 0, 92, -188]\) \(21296/15\) \(-60000000\) \([4]\) \(192\) \(0.18097\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 600.a have rank \(0\).

Complex multiplication

The elliptic curves in class 600.a do not have complex multiplication.

Modular form 600.2.a.a

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