E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 21315.p
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
21315.p1 |
21315c4 |
[1,1,0,−12618,532323] |
1888690601881/31827645 |
3744490606605 |
[2] |
55296 |
1.2106
|
|
21315.p2 |
21315c2 |
[1,1,0,−1593,−12312] |
3803721481/1703025 |
200359188225 |
[2,2] |
27648 |
0.86403
|
|
21315.p3 |
21315c1 |
[1,1,0,−1348,−19613] |
2305199161/1305 |
153531945 |
[2] |
13824 |
0.51746
|
Γ0(N)-optimal |
21315.p4 |
21315c3 |
[1,1,0,5512,−84783] |
157376536199/118918125 |
−13990598488125 |
[2] |
55296 |
1.2106
|
|
The elliptic curves in class 21315.p have
rank 1.
The elliptic curves in class 21315.p 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.
⎝⎜⎜⎛1244212242144241⎠⎟⎟⎞
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.