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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 38640.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.bn1 | 38640cb4 | \([0, -1, 0, -70880, 7264320]\) | \(9614816895690721/34652610405\) | \(141937092218880\) | \([2]\) | \(131072\) | \(1.5767\) | |
| 38640.bn2 | 38640cb2 | \([0, -1, 0, -6480, 0]\) | \(7347774183121/4251692025\) | \(17414930534400\) | \([2, 2]\) | \(65536\) | \(1.2302\) | |
| 38640.bn3 | 38640cb1 | \([0, -1, 0, -4480, -113600]\) | \(2428257525121/8150625\) | \(33384960000\) | \([2]\) | \(32768\) | \(0.88359\) | \(\Gamma_0(N)\)-optimal |
| 38640.bn4 | 38640cb3 | \([0, -1, 0, 25920, -25920]\) | \(470166844956479/272118787605\) | \(-1114598554030080\) | \([4]\) | \(131072\) | \(1.5767\) |
Rank
sage: E.rank()
The elliptic curves in class 38640.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 38640.bn do not have complex multiplication.Modular form 38640.2.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.
