Properties

Label 187395h
Number of curves 88
Conductor 187395187395
CM no
Rank 11
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 187395h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187395.g6 187395h1 [1,1,1,105730,13276258][1, 1, 1, -105730, -13276258] 147281603041/5265147281603041/5265 46727068804654672706880465 [2][2] 691200691200 1.52011.5201 Γ0(N)\Gamma_0(N)-optimal
187395.g5 187395h2 [1,1,1,110535,12009660][1, 1, 1, -110535, -12009660] 168288035761/27720225168288035761/27720225 2460180172564822524601801725648225 [2,2][2, 2] 13824001382400 1.86671.8667  
187395.g4 187395h3 [1,1,1,499740,124367772][1, 1, 1, -499740, 124367772] 15551989015681/144590062515551989015681/1445900625 12832421270477006251283242127047700625 [2,2][2, 2] 27648002764800 2.21332.2133  
187395.g7 187395h4 [1,1,1,201790,67228720][1, 1, 1, 201790, -67228720] 1023887723039/27980368651023887723039/2798036865 2483268017261200065-2483268017261200065 [2][2] 27648002764800 2.21332.2133  
187395.g2 187395h5 [1,1,1,7808145,8394558870][1, 1, 1, -7808145, 8394558870] 59319456301170001/59414062559319456301170001/594140625 527301991719140625527301991719140625 [2,2][2, 2] 55296005529600 2.55982.5598  
187395.g8 187395h6 [1,1,1,581385,590116422][1, 1, 1, 581385, 590116422] 24487529386319/18353941222524487529386319/183539412225 162891903958263900225-162891903958263900225 [2][2] 55296005529600 2.55982.5598  
187395.g1 187395h7 [1,1,1,124930020,537410643870][1, 1, 1, -124930020, 537410643870] 242970740812818720001/24375242970740812818720001/24375 2163290222437521632902224375 [2][2] 1105920011059200 2.90642.9064  
187395.g3 187395h8 [1,1,1,7620750,8816872242][1, 1, 1, -7620750, 8816872242] 55150149867714721/5950927734375-55150149867714721/5950927734375 5281470269622802734375-5281470269622802734375 [2][2] 1105920011059200 2.90642.9064  

Rank

sage: E.rank()
 

The elliptic curves in class 187395h have rank 11.

Complex multiplication

The elliptic curves in class 187395h do not have complex multiplication.

Modular form 187395.2.a.h

sage: E.q_eigenform(10)
 
qq2q3q4+q5+q6+3q8+q9q104q11+q12q13q15q162q17q184q19+O(q20)q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} + 3 q^{8} + q^{9} - q^{10} - 4 q^{11} + q^{12} - q^{13} - q^{15} - q^{16} - 2 q^{17} - q^{18} - 4 q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the Cremona numbering.

(124488161621224488421422444241881616842814228428418816841628141684162841)\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.