Show commands:
SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 33600.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33600.bd1 | 33600ed4 | \([0, -1, 0, -15233, -717663]\) | \(381775972/567\) | \(580608000000\) | \([2]\) | \(65536\) | \(1.1583\) | |
| 33600.bd2 | 33600ed2 | \([0, -1, 0, -1233, -3663]\) | \(810448/441\) | \(112896000000\) | \([2, 2]\) | \(32768\) | \(0.81168\) | |
| 33600.bd3 | 33600ed1 | \([0, -1, 0, -733, 7837]\) | \(2725888/21\) | \(336000000\) | \([2]\) | \(16384\) | \(0.46510\) | \(\Gamma_0(N)\)-optimal |
| 33600.bd4 | 33600ed3 | \([0, -1, 0, 4767, -33663]\) | \(11696828/7203\) | \(-7375872000000\) | \([2]\) | \(65536\) | \(1.1583\) |
Rank
sage: E.rank()
The elliptic curves in class 33600.bd have rank \(2\).
Complex multiplication
The elliptic curves in class 33600.bd do not have complex multiplication.Modular form 33600.2.a.bd
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.
