E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 20070.be
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
20070.be1 |
20070bg3 |
[1,−1,1,−757697342,−7799122947891] |
65990812340278189764070806169/2142150634958771454912000 |
1561627812884944390630848000 |
[2] |
11073024 |
3.9917
|
|
20070.be2 |
20070bg2 |
[1,−1,1,−115457342,308001020109] |
233486000400975208694166169/78913673205682176000000 |
57528067766942306304000000 |
[2,2] |
5536512 |
3.6452
|
|
20070.be3 |
20070bg1 |
[1,−1,1,−103660862,406176045261] |
168982070711351853939176089/37703877214076928000 |
27486126489062080512000 |
[4] |
2768256 |
3.2986
|
Γ0(N)-optimal |
20070.be4 |
20070bg4 |
[1,−1,1,338038978,2131781820621] |
5859985279907178462243106151/6084442029900375000000000 |
−4435558239797373375000000000 |
[2] |
11073024 |
3.9917
|
|
The elliptic curves in class 20070.be have
rank 0.
The elliptic curves in class 20070.be do not have complex multiplication.
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.