sage:E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 51984cq
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
51984.z2 |
51984cq1 |
[0,0,0,1022352,454449904] |
841232384/1121931 |
−157606901180488986624 |
[] |
1382400 |
2.5614
|
Γ0(N)-optimal |
51984.z1 |
51984cq2 |
[0,0,0,−228227088,1327088209264] |
−9358714467168256/22284891 |
−3130542443033456062464 |
[] |
6912000 |
3.3661
|
|
sage:E.rank()
The elliptic curves in class 51984cq have
rank 0.
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1 |
3 | 1 |
19 | 1 |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
5 |
1−3T+5T2 |
1.5.ad
|
7 |
1−5T+7T2 |
1.7.af
|
11 |
1−T+11T2 |
1.11.ab
|
13 |
1+2T+13T2 |
1.13.c
|
17 |
1−T+17T2 |
1.17.ab
|
23 |
1+4T+23T2 |
1.23.e
|
29 |
1+2T+29T2 |
1.29.c
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 51984cq 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 Cremona numbering.
(1551)
sage:E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.