Show commands:
SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 84150.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84150.bv1 | 84150cc4 | \([1, -1, 0, -127788192, -555980084784]\) | \(20260414982443110947641/720358602480\) | \(8205334706373750000\) | \([2]\) | \(7077888\) | \(3.1251\) | |
| 84150.bv2 | 84150cc2 | \([1, -1, 0, -7998192, -8659574784]\) | \(4967657717692586041/29490113030400\) | \(335910818736900000000\) | \([2, 2]\) | \(3538944\) | \(2.7785\) | |
| 84150.bv3 | 84150cc3 | \([1, -1, 0, -3408192, -18532664784]\) | \(-384369029857072441/12804787777021680\) | \(-145854535772637573750000\) | \([2]\) | \(7077888\) | \(3.1251\) | |
| 84150.bv4 | 84150cc1 | \([1, -1, 0, -798192, 45225216]\) | \(4937402992298041/2780405760000\) | \(31670559360000000000\) | \([2]\) | \(1769472\) | \(2.4319\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 84150.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 84150.bv do not have complex multiplication.Modular form 84150.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
