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] |
2361739090258884097/5202 |
5202 |
[2] |
128 |
0.84708
|
|
102.c2 |
102b3 |
[1,0,0,−1734,−27936] |
576615941610337/27060804 |
27060804 |
[2,2] |
64 |
0.50050
|
|
102.c3 |
102b6 |
[1,0,0,−1644,−30942] |
−491411892194497/125563633938 |
−125563633938 |
[2] |
128 |
0.84708
|
|
102.c4 |
102b2 |
[1,0,0,−114,−396] |
163936758817/30338064 |
30338064 |
[2,4] |
32 |
0.15393
|
|
102.c5 |
102b1 |
[1,0,0,−34,68] |
4354703137/352512 |
352512 |
[8] |
16 |
−0.19264
|
Γ0(N)-optimal |
102.c6 |
102b4 |
[1,0,0,226,−2232] |
1276229915423/2927177028 |
−2927177028 |
[4] |
64 |
0.50050
|
|
The elliptic curves in class 102.c have
rank 0.
The elliptic curves in class 102.c do not have complex multiplication.
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.
⎝⎜⎜⎜⎜⎜⎜⎛124488212244421488424122848214848241⎠⎟⎟⎟⎟⎟⎟⎞
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.