Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 15210.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15210.bj1 | 15210ba4 | \([1, -1, 1, -764588, 154326007]\) | \(520300455507/193072360\) | \(18343048378631740920\) | \([2]\) | \(580608\) | \(2.3963\) | |
| 15210.bj2 | 15210ba2 | \([1, -1, 1, -675863, 214032017]\) | \(261984288445803/42250\) | \(5506182366750\) | \([2]\) | \(193536\) | \(1.8470\) | |
| 15210.bj3 | 15210ba1 | \([1, -1, 1, -42113, 3373517]\) | \(-63378025803/812500\) | \(-105888122437500\) | \([2]\) | \(96768\) | \(1.5004\) | \(\Gamma_0(N)\)-optimal |
| 15210.bj4 | 15210ba3 | \([1, -1, 1, 148012, 17070967]\) | \(3774555693/3515200\) | \(-333965377854014400\) | \([2]\) | \(290304\) | \(2.0497\) |
Rank
sage: E.rank()
The elliptic curves in class 15210.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 15210.bj do not have complex multiplication.Modular form 15210.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
