Show commands:
SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 51520.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51520.bo1 | 51520be4 | \([0, 0, 0, -2342252, 1379743664]\) | \(5421065386069310769/1919709260\) | \(503240264253440\) | \([2]\) | \(589824\) | \(2.1754\) | |
| 51520.bo2 | 51520be2 | \([0, 0, 0, -147052, 21353904]\) | \(1341518286067569/24894528400\) | \(6525951252889600\) | \([2, 2]\) | \(294912\) | \(1.8289\) | |
| 51520.bo3 | 51520be1 | \([0, 0, 0, -19052, -508496]\) | \(2917464019569/1262240000\) | \(330888642560000\) | \([2]\) | \(147456\) | \(1.4823\) | \(\Gamma_0(N)\)-optimal |
| 51520.bo4 | 51520be3 | \([0, 0, 0, 148, 62157744]\) | \(1367631/6366992112460\) | \(-1669068780328714240\) | \([2]\) | \(589824\) | \(2.1754\) |
Rank
sage: E.rank()
The elliptic curves in class 51520.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 51520.bo do not have complex multiplication.Modular form 51520.2.a.bo
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.
