Show commands:
SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 15600bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.bk4 | 15600bd1 | \([0, -1, 0, -7808, -5541888]\) | \(-822656953/207028224\) | \(-13249806336000000\) | \([2]\) | \(122880\) | \(1.7728\) | \(\Gamma_0(N)\)-optimal |
| 15600.bk3 | 15600bd2 | \([0, -1, 0, -519808, -142757888]\) | \(242702053576633/2554695936\) | \(163500539904000000\) | \([2, 2]\) | \(245760\) | \(2.1194\) | |
| 15600.bk1 | 15600bd3 | \([0, -1, 0, -8295808, -9194021888]\) | \(986551739719628473/111045168\) | \(7106890752000000\) | \([2]\) | \(491520\) | \(2.4659\) | |
| 15600.bk2 | 15600bd4 | \([0, -1, 0, -935808, 118490112]\) | \(1416134368422073/725251155408\) | \(46416073946112000000\) | \([2]\) | \(491520\) | \(2.4659\) |
Rank
sage: E.rank()
The elliptic curves in class 15600bd have rank \(0\).
Complex multiplication
The elliptic curves in class 15600bd do not have complex multiplication.Modular form 15600.2.a.bd
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 Cremona 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 Cremona labels.
