Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 115920.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.bw1 | 115920dh4 | \([0, 0, 0, -637923, -195498718]\) | \(9614816895690721/34652610405\) | \(103472140227563520\) | \([2]\) | \(1048576\) | \(2.1260\) | |
| 115920.bw2 | 115920dh2 | \([0, 0, 0, -58323, 58322]\) | \(7347774183121/4251692025\) | \(12695484359577600\) | \([2, 2]\) | \(524288\) | \(1.7795\) | |
| 115920.bw3 | 115920dh1 | \([0, 0, 0, -40323, 3107522]\) | \(2428257525121/8150625\) | \(24337635840000\) | \([2]\) | \(262144\) | \(1.4329\) | \(\Gamma_0(N)\)-optimal |
| 115920.bw4 | 115920dh3 | \([0, 0, 0, 233277, 466562]\) | \(470166844956479/272118787605\) | \(-812542345887928320\) | \([2]\) | \(1048576\) | \(2.1260\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 115920.bw do not have complex multiplication.Modular form 115920.2.a.bw
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.
