Properties

Label 28050.cx
Number of curves $8$
Conductor $28050$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28050.cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28050.cx1 28050cm8 \([1, 1, 1, -5030912063, -137348787904219]\) \(901247067798311192691198986281/552431869440\) \(8631747960000000\) \([2]\) \(15925248\) \(3.7655\)  
28050.cx2 28050cm7 \([1, 1, 1, -316544063, -2115881920219]\) \(224494757451893010998773801/6152490825146276160000\) \(96132669142910565000000000\) \([2]\) \(15925248\) \(3.7655\)  
28050.cx3 28050cm6 \([1, 1, 1, -314432063, -2146172224219]\) \(220031146443748723000125481/172266701724057600\) \(2691667214438400000000\) \([2, 2]\) \(7962624\) \(3.4189\)  
28050.cx4 28050cm5 \([1, 1, 1, -62122688, -188349461719]\) \(1696892787277117093383481/1440538624914939000\) \(22508416014295921875000\) \([2]\) \(5308416\) \(3.2162\)  
28050.cx5 28050cm4 \([1, 1, 1, -40684688, 98799642281]\) \(476646772170172569823801/5862293314453125000\) \(91598333038330078125000\) \([2]\) \(5308416\) \(3.2162\)  
28050.cx6 28050cm3 \([1, 1, 1, -19520063, -34012480219]\) \(-52643812360427830814761/1504091705903677440\) \(-23501432904744960000000\) \([2]\) \(3981312\) \(3.0724\)  
28050.cx7 28050cm2 \([1, 1, 1, -4747688, -1536461719]\) \(757443433548897303481/373234243041000000\) \(5831785047515625000000\) \([2, 2]\) \(2654208\) \(2.8696\)  
28050.cx8 28050cm1 \([1, 1, 1, 1084312, -183437719]\) \(9023321954633914439/6156756739584000\) \(-96199324056000000000\) \([2]\) \(1327104\) \(2.5231\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 28050.cx have rank \(0\).

Complex multiplication

The elliptic curves in class 28050.cx do not have complex multiplication.

Modular form 28050.2.a.cx

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

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 3 & 12 & 4 & 6 & 12 \\ 4 & 1 & 2 & 12 & 3 & 4 & 6 & 12 \\ 2 & 2 & 1 & 6 & 6 & 2 & 3 & 6 \\ 3 & 12 & 6 & 1 & 4 & 12 & 2 & 4 \\ 12 & 3 & 6 & 4 & 1 & 12 & 2 & 4 \\ 4 & 4 & 2 & 12 & 12 & 1 & 6 & 3 \\ 6 & 6 & 3 & 2 & 2 & 6 & 1 & 2 \\ 12 & 12 & 6 & 4 & 4 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.