sage:E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 462.c
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
462.c1 |
462b3 |
[1,1,0,−92004,10703088] |
86129359107301290313/9166294368 |
9166294368 |
[2] |
1920 |
1.3393
|
|
462.c2 |
462b2 |
[1,1,0,−5764,164560] |
21184262604460873/216872764416 |
216872764416 |
[2,2] |
960 |
0.99273
|
|
462.c3 |
462b4 |
[1,1,0,−1444,410800] |
−333345918055753/72923718045024 |
−72923718045024 |
[2] |
1920 |
1.3393
|
|
462.c4 |
462b1 |
[1,1,0,−644,−2352] |
29609739866953/15259926528 |
15259926528 |
[2] |
480 |
0.64616
|
Γ0(N)-optimal |
sage:E.rank()
The elliptic curves in class 462.c have
rank 0.
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1+T |
3 | 1+T |
7 | 1+T |
11 | 1−T |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
5 |
1−2T+5T2 |
1.5.ac
|
13 |
1−2T+13T2 |
1.13.ac
|
17 |
1−6T+17T2 |
1.17.ag
|
19 |
1+8T+19T2 |
1.19.i
|
23 |
1−4T+23T2 |
1.23.ae
|
29 |
1−2T+29T2 |
1.29.ac
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 462.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.
⎝⎜⎜⎛1244212242144241⎠⎟⎟⎞
sage:E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.