Show commands:
SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 46200bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46200.h3 | 46200bu1 | \([0, -1, 0, -3508, -76988]\) | \(1193895376/31185\) | \(124740000000\) | \([2]\) | \(49152\) | \(0.91073\) | \(\Gamma_0(N)\)-optimal |
| 46200.h2 | 46200bu2 | \([0, -1, 0, -8008, 166012]\) | \(3550014724/1334025\) | \(21344400000000\) | \([2, 2]\) | \(98304\) | \(1.2573\) | |
| 46200.h4 | 46200bu3 | \([0, -1, 0, 24992, 1156012]\) | \(53946017998/49520625\) | \(-1584660000000000\) | \([2]\) | \(196608\) | \(1.6039\) | |
| 46200.h1 | 46200bu4 | \([0, -1, 0, -113008, 14656012]\) | \(4987755354962/1537305\) | \(49193760000000\) | \([2]\) | \(196608\) | \(1.6039\) |
Rank
sage: E.rank()
The elliptic curves in class 46200bu have rank \(0\).
Complex multiplication
The elliptic curves in class 46200bu do not have complex multiplication.Modular form 46200.2.a.bu
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 Cremona 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 Cremona labels.
