Show commands:
SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 9408.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9408.bd1 | 9408bz3 | \([0, -1, 0, -22017, 1185633]\) | \(306182024/21609\) | \(83305340633088\) | \([2]\) | \(24576\) | \(1.4185\) | |
| 9408.bd2 | 9408bz2 | \([0, -1, 0, -4377, -87975]\) | \(19248832/3969\) | \(1912622616576\) | \([2, 2]\) | \(12288\) | \(1.0719\) | |
| 9408.bd3 | 9408bz1 | \([0, -1, 0, -4132, -100862]\) | \(1036433728/63\) | \(474360768\) | \([2]\) | \(6144\) | \(0.72533\) | \(\Gamma_0(N)\)-optimal |
| 9408.bd4 | 9408bz4 | \([0, -1, 0, 9343, -540735]\) | \(23393656/45927\) | \(-177054207934464\) | \([2]\) | \(24576\) | \(1.4185\) |
Rank
sage: E.rank()
The elliptic curves in class 9408.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 9408.bd do not have complex multiplication.Modular form 9408.2.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 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.
