Properties

Label 600.h
Number of curves 6
Conductor 600
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("600.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 600.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
600.h1 600d5 [0, 1, 0, -9608, -365712] [2] 512  
600.h2 600d4 [0, 1, 0, -1608, 24288] [2] 256  
600.h3 600d3 [0, 1, 0, -608, -5712] [2, 2] 256  
600.h4 600d2 [0, 1, 0, -108, 288] [2, 2] 128  
600.h5 600d1 [0, 1, 0, 17, 38] [2] 64 \(\Gamma_0(N)\)-optimal
600.h6 600d6 [0, 1, 0, 392, -21712] [2] 512  

Rank

sage: E.rank()
 

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

Modular form 600.2.a.h

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{9} + 4q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.