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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 9408.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9408.bj1 | 9408k3 | \([0, -1, 0, -6337, 196225]\) | \(7301384/3\) | \(11565367296\) | \([2]\) | \(9216\) | \(0.89331\) | |
| 9408.bj2 | 9408k2 | \([0, -1, 0, -457, 2185]\) | \(21952/9\) | \(4337012736\) | \([2, 2]\) | \(4608\) | \(0.54673\) | |
| 9408.bj3 | 9408k1 | \([0, -1, 0, -212, -1098]\) | \(140608/3\) | \(22588608\) | \([2]\) | \(2304\) | \(0.20016\) | \(\Gamma_0(N)\)-optimal |
| 9408.bj4 | 9408k4 | \([0, -1, 0, 1503, 14337]\) | \(97336/81\) | \(-312264916992\) | \([2]\) | \(9216\) | \(0.89331\) |
Rank
sage: E.rank()
The elliptic curves in class 9408.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 9408.bj do not have complex multiplication.Modular form 9408.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
