Properties

Label 1050c
Number of curves 8
Conductor 1050
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1050.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1050c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1050.c7 1050c1 [1, 1, 0, 5250, 112500] [2] 3072 \(\Gamma_0(N)\)-optimal
1050.c6 1050c2 [1, 1, 0, -26750, 976500] [2, 2] 6144  
1050.c5 1050c3 [1, 1, 0, -188750, -30937500] [2, 2] 12288  
1050.c4 1050c4 [1, 1, 0, -376750, 88826500] [2] 12288  
1050.c2 1050c5 [1, 1, 0, -3001250, -2002500000] [2, 2] 24576  
1050.c8 1050c6 [1, 1, 0, 31750, -98631000] [2] 24576  
1050.c1 1050c7 [1, 1, 0, -48020000, -128100018750] [2] 49152  
1050.c3 1050c8 [1, 1, 0, -2982500, -2028731250] [2] 49152  

Rank

sage: E.rank()
 

The elliptic curves in class 1050c have rank \(0\).

Modular form 1050.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} - 4q^{11} - q^{12} + 2q^{13} - q^{14} + q^{16} - 2q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.