sage:E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 46800.fh
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
46800.fh1 |
46800v4 |
[0,0,0,−126360075,−546717437750] |
19129597231400697604/26325 |
307054800000000 |
[2] |
2359296 |
2.9461
|
|
46800.fh2 |
46800v2 |
[0,0,0,−7897575,−8542300250] |
18681746265374416/693005625 |
2020804402500000000 |
[2,2] |
1179648 |
2.5996
|
|
46800.fh3 |
46800v3 |
[0,0,0,−7533075,−9366434750] |
−4053153720264484/903687890625 |
−10540615556250000000000 |
[2] |
2359296 |
2.9461
|
|
46800.fh4 |
46800v1 |
[0,0,0,−516450,−120436625] |
83587439220736/13990184325 |
2549711093231250000 |
[2] |
589824 |
2.2530
|
Γ0(N)-optimal |
sage:E.rank()
The elliptic curves in class 46800.fh have
rank 0.
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1 |
3 | 1 |
5 | 1 |
13 | 1+T |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
7 |
1−4T+7T2 |
1.7.ae
|
11 |
1+11T2 |
1.11.a
|
17 |
1−2T+17T2 |
1.17.ac
|
19 |
1+19T2 |
1.19.a
|
23 |
1+23T2 |
1.23.a
|
29 |
1−2T+29T2 |
1.29.ac
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 46800.fh 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.