sage:E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 144150cc
sage:E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
144150.dh3 |
144150cc1 |
[1,1,1,−2607213,1439514531] |
141339344329/17141760 |
237708985919040000000 |
[4] |
6635520 |
2.6403
|
Γ0(N)-optimal |
144150.dh2 |
144150cc2 |
[1,1,1,−10295213,−11214933469] |
8702409880009/1120910400 |
15543939157362225000000 |
[2,2] |
13271040 |
2.9869
|
|
144150.dh4 |
144150cc3 |
[1,1,1,15651787,−58594155469] |
30579142915511/124675335000 |
−1728903417850127109375000 |
[2] |
26542080 |
3.3334
|
|
144150.dh1 |
144150cc4 |
[1,1,1,−159250213,−773566623469] |
32208729120020809/658986840 |
9138331972352469375000 |
[2] |
26542080 |
3.3334
|
|
sage:E.rank()
The elliptic curves in class 144150cc have
rank 1.
|
Bad L-factors: |
Prime |
L-Factor |
2 | 1+T |
3 | 1−T |
5 | 1 |
31 | 1 |
|
|
Good L-factors: |
Prime |
L-Factor |
Isogeny Class over Fp |
7 |
1−T+7T2 |
1.7.ab
|
11 |
1+5T+11T2 |
1.11.f
|
13 |
1−4T+13T2 |
1.13.ae
|
17 |
1+2T+17T2 |
1.17.c
|
19 |
1+2T+19T2 |
1.19.c
|
23 |
1+4T+23T2 |
1.23.e
|
29 |
1+3T+29T2 |
1.29.d
|
⋯ | ⋯ | ⋯ |
|
|
See L-function page for more information |
The elliptic curves in class 144150cc 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.
⎝⎜⎜⎛1244212242144241⎠⎟⎟⎞
sage:E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.