Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 333200.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 333200.bb1 | 333200bb2 | \([0, 1, 0, -2519008, -293136012]\) | \(234770924809/130960928\) | \(986075021969408000000\) | \([2]\) | \(14745600\) | \(2.7187\) | |
| 333200.bb2 | 333200bb1 | \([0, 1, 0, 616992, -35984012]\) | \(3449795831/2071552\) | \(-15597825359872000000\) | \([2]\) | \(7372800\) | \(2.3721\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 333200.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 333200.bb do not have complex multiplication.Modular form 333200.2.a.bb
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
