Show commands:
SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 9360.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9360.bn1 | 9360bs3 | \([0, 0, 0, -69627, -7070294]\) | \(12501706118329/2570490\) | \(7675442012160\) | \([2]\) | \(24576\) | \(1.4695\) | |
| 9360.bn2 | 9360bs2 | \([0, 0, 0, -4827, -84854]\) | \(4165509529/1368900\) | \(4087513497600\) | \([2, 2]\) | \(12288\) | \(1.1229\) | |
| 9360.bn3 | 9360bs1 | \([0, 0, 0, -1947, 32074]\) | \(273359449/9360\) | \(27948810240\) | \([2]\) | \(6144\) | \(0.77634\) | \(\Gamma_0(N)\)-optimal |
| 9360.bn4 | 9360bs4 | \([0, 0, 0, 13893, -582806]\) | \(99317171591/106616250\) | \(-318354416640000\) | \([2]\) | \(24576\) | \(1.4695\) |
Rank
sage: E.rank()
The elliptic curves in class 9360.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 9360.bn do not have complex multiplication.Modular form 9360.2.a.bn
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.
