Show commands:
SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 57222.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57222.bs1 | 57222bt4 | \([1, -1, 1, -1258726694, -17188100264599]\) | \(12534210458299016895673/315581882565708\) | \(5553069630407582261328108\) | \([2]\) | \(35389440\) | \(3.8562\) | |
| 57222.bs2 | 57222bt2 | \([1, -1, 1, -81670154, -246960895687]\) | \(3423676911662954233/483711578981136\) | \(8511528156428211405921936\) | \([2, 2]\) | \(17694720\) | \(3.5096\) | |
| 57222.bs3 | 57222bt1 | \([1, -1, 1, -21535034, 34615790201]\) | \(62768149033310713/6915442583808\) | \(121686117975976630526208\) | \([2]\) | \(8847360\) | \(3.1630\) | \(\Gamma_0(N)\)-optimal |
| 57222.bs4 | 57222bt3 | \([1, -1, 1, 133224466, -1327451045047]\) | \(14861225463775641287/51859390496937804\) | \(-912532760368562008380929004\) | \([2]\) | \(35389440\) | \(3.8562\) |
Rank
sage: E.rank()
The elliptic curves in class 57222.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 57222.bs do not have complex multiplication.Modular form 57222.2.a.bs
sage: E.q_eigenform(10)
Isogeny matrix
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
