Properties

Label 1200.e
Number of curves 8
Conductor 1200
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("1200.e1")
sage: E.isogeny_class()

Elliptic curves in class 1200.e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1200.e1 1200j7 [0, -1, 0, -864008, 309406512] 4 6144  
1200.e2 1200j5 [0, -1, 0, -54008, 4846512] 4 3072  
1200.e3 1200j8 [0, -1, 0, -44008, 6686512] 2 6144  
1200.e4 1200j3 [0, -1, 0, -32008, -2193488] 2 1536  
1200.e5 1200j4 [0, -1, 0, -4008, 46512] 4 1536  
1200.e6 1200j2 [0, -1, 0, -2008, -33488] 4 768  
1200.e7 1200j1 [0, -1, 0, -8, -1488] 2 384 \(\Gamma_0(N)\)-optimal
1200.e8 1200j6 [0, -1, 0, 13992, 334512] 2 3072  

Rank

sage: E.rank()

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

Modular form 1200.2.a.e

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.