sage:E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4235.c
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
4235.c1 |
4235b3 |
[0,1,1,−15891,801301] |
−250523582464/13671875 |
−24220560546875 |
[] |
8100 |
1.3264
|
|
4235.c2 |
4235b1 |
[0,1,1,−161,−929] |
−262144/35 |
−62004635 |
[] |
900 |
0.22780
|
Γ0(N)-optimal |
4235.c3 |
4235b2 |
[0,1,1,1049,2580] |
71991296/42875 |
−75955677875 |
[] |
2700 |
0.77710
|
|
sage:E.rank()
The elliptic curves in class 4235.c have
rank 0.
|
Bad L-factors: |
Prime |
L-Factor |
5 | 1+T |
7 | 1+T |
11 | 1 |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
2 |
1+2T2 |
1.2.a
|
3 |
1−T+3T2 |
1.3.ab
|
13 |
1+5T+13T2 |
1.13.f
|
17 |
1+3T+17T2 |
1.17.d
|
19 |
1+2T+19T2 |
1.19.c
|
23 |
1+6T+23T2 |
1.23.g
|
29 |
1+3T+29T2 |
1.29.d
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 4235.c do not have complex multiplication.
sage:E.q_eigenform(10)
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.
⎝⎛193913331⎠⎞
sage:E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.