Properties

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

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

Elliptic curves in class 1050.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.c1 1050c7 \([1, 1, 0, -48020000, -128100018750]\) \(783736670177727068275201/360150\) \(5627343750\) \([2]\) \(49152\) \(2.5991\)  
1050.c2 1050c5 \([1, 1, 0, -3001250, -2002500000]\) \(191342053882402567201/129708022500\) \(2026687851562500\) \([2, 2]\) \(24576\) \(2.2526\)  
1050.c3 1050c8 \([1, 1, 0, -2982500, -2028731250]\) \(-187778242790732059201/4984939585440150\) \(-77889681022502343750\) \([2]\) \(49152\) \(2.5991\)  
1050.c4 1050c4 \([1, 1, 0, -376750, 88826500]\) \(378499465220294881/120530818800\) \(1883294043750000\) \([2]\) \(12288\) \(1.9060\)  
1050.c5 1050c3 \([1, 1, 0, -188750, -30937500]\) \(47595748626367201/1215506250000\) \(18992285156250000\) \([2, 2]\) \(12288\) \(1.9060\)  
1050.c6 1050c2 \([1, 1, 0, -26750, 976500]\) \(135487869158881/51438240000\) \(803722500000000\) \([2, 2]\) \(6144\) \(1.5594\)  
1050.c7 1050c1 \([1, 1, 0, 5250, 112500]\) \(1023887723039/928972800\) \(-14515200000000\) \([2]\) \(3072\) \(1.2129\) \(\Gamma_0(N)\)-optimal
1050.c8 1050c6 \([1, 1, 0, 31750, -98631000]\) \(226523624554079/269165039062500\) \(-4205703735351562500\) \([2]\) \(24576\) \(2.2526\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 1050.c do not have complex multiplication.

Modular form 1050.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.