E = EllipticCurve("qq1")
E.isogeny_class()
Elliptic curves in class 235200qq
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
235200.qq4 |
235200qq1 |
[0,1,0,−1416508,977960738] |
−2671731885376/1969120125 |
−231665013586125000000 |
[2] |
7077888 |
2.6071
|
Γ0(N)-optimal |
235200.qq3 |
235200qq2 |
[0,1,0,−25726633,50205963863] |
250094631024064/62015625 |
466948881000000000000 |
[2,2] |
14155776 |
2.9536
|
|
235200.qq1 |
235200qq3 |
[0,1,0,−411601633,3213995088863] |
128025588102048008/7875 |
474360768000000000 |
[2] |
28311552 |
3.3002
|
|
235200.qq2 |
235200qq4 |
[0,1,0,−28813633,37398000863] |
43919722445768/15380859375 |
926485875000000000000000 |
[2] |
28311552 |
3.3002
|
|
The elliptic curves in class 235200qq have
rank 1.
The elliptic curves in class 235200qq 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 Cremona numbering.
⎝⎜⎜⎛1244212242144241⎠⎟⎟⎞
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.