Properties

Label 102.c
Number of curves 66
Conductor 102102
CM no
Rank 00
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 102.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102.c1 102b5 [1,0,0,27744,1781010][1, 0, 0, -27744, -1781010] 2361739090258884097/52022361739090258884097/5202 52025202 [2][2] 128128 0.847080.84708  
102.c2 102b3 [1,0,0,1734,27936][1, 0, 0, -1734, -27936] 576615941610337/27060804576615941610337/27060804 2706080427060804 [2,2][2, 2] 6464 0.500500.50050  
102.c3 102b6 [1,0,0,1644,30942][1, 0, 0, -1644, -30942] 491411892194497/125563633938-491411892194497/125563633938 125563633938-125563633938 [2][2] 128128 0.847080.84708  
102.c4 102b2 [1,0,0,114,396][1, 0, 0, -114, -396] 163936758817/30338064163936758817/30338064 3033806430338064 [2,4][2, 4] 3232 0.153930.15393  
102.c5 102b1 [1,0,0,34,68][1, 0, 0, -34, 68] 4354703137/3525124354703137/352512 352512352512 [8][8] 1616 0.19264-0.19264 Γ0(N)\Gamma_0(N)-optimal
102.c6 102b4 [1,0,0,226,2232][1, 0, 0, 226, -2232] 1276229915423/29271770281276229915423/2927177028 2927177028-2927177028 [4][4] 6464 0.500500.50050  

Rank

sage: E.rank()
 

The elliptic curves in class 102.c have rank 00.

Complex multiplication

The elliptic curves in class 102.c do not have complex multiplication.

Modular form 102.2.a.c

sage: E.q_eigenform(10)
 
q+q2+q3+q42q5+q6+q8+q92q104q11+q122q132q15+q16+q17+q18+4q19+O(q20)q + q^{2} + q^{3} + q^{4} - 2 q^{5} + q^{6} + q^{8} + q^{9} - 2 q^{10} - 4 q^{11} + q^{12} - 2 q^{13} - 2 q^{15} + 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,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 LMFDB numbering.

(124488212244421488424122848214848241)\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.