Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 38640.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.bj1 | 38640m4 | \([0, -1, 0, -171760, -27341600]\) | \(273629163383866082/26408025\) | \(54083635200\) | \([2]\) | \(163840\) | \(1.4932\) | |
| 38640.bj2 | 38640m3 | \([0, -1, 0, -19040, 326112]\) | \(372749784765122/194143359375\) | \(397605600000000\) | \([4]\) | \(163840\) | \(1.4932\) | |
| 38640.bj3 | 38640m2 | \([0, -1, 0, -10760, -422400]\) | \(134555337776164/1312250625\) | \(1343744640000\) | \([2, 2]\) | \(81920\) | \(1.1467\) | |
| 38640.bj4 | 38640m1 | \([0, -1, 0, -180, -16128]\) | \(-2533446736/440749575\) | \(-112831891200\) | \([2]\) | \(40960\) | \(0.80010\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38640.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 38640.bj do not have complex multiplication.Modular form 38640.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
