Properties

Label 600.c
Number of curves 6
Conductor 600
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("600.c1")
sage: E.isogeny_class()

Elliptic curves in class 600.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
600.c1 600a5 [0, -1, 0, -80008, -8683988] 2 1536  
600.c2 600a3 [0, -1, 0, -5008, -133988] 4 768  
600.c3 600a6 [0, -1, 0, -2008, -295988] 2 1536  
600.c4 600a2 [0, -1, 0, -508, 1012] 4 384  
600.c5 600a1 [0, -1, 0, -383, 3012] 4 192 \(\Gamma_0(N)\)-optimal
600.c6 600a4 [0, -1, 0, 1992, 6012] 2 768  

Rank

sage: E.rank()

The elliptic curves in class 600.c have rank \(1\).

Modular form 600.2.a.c

sage: E.q_eigenform(10)
\( q - q^{3} + q^{9} - 4q^{11} - 6q^{13} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.