Show commands:
SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 16650.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16650.bv1 | 16650bz3 | \([1, -1, 1, -1186880, 497985747]\) | \(16232905099479601/4052240\) | \(46157546250000\) | \([2]\) | \(165888\) | \(1.9975\) | |
| 16650.bv2 | 16650bz4 | \([1, -1, 1, -1182380, 501945747]\) | \(-16048965315233521/256572640900\) | \(-2922522737751562500\) | \([2]\) | \(331776\) | \(2.3441\) | |
| 16650.bv3 | 16650bz1 | \([1, -1, 1, -16880, 465747]\) | \(46694890801/18944000\) | \(215784000000000\) | \([2]\) | \(55296\) | \(1.4482\) | \(\Gamma_0(N)\)-optimal |
| 16650.bv4 | 16650bz2 | \([1, -1, 1, 55120, 3345747]\) | \(1625964918479/1369000000\) | \(-15593765625000000\) | \([2]\) | \(110592\) | \(1.7948\) |
Rank
sage: E.rank()
The elliptic curves in class 16650.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 16650.bv do not have complex multiplication.Modular form 16650.2.a.bv
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
