Show commands:
SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 37026.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37026.bp1 | 37026bd1 | \([1, -1, 1, -984479, 373248263]\) | \(81706955619457/744505344\) | \(961504804525326336\) | \([2]\) | \(1075200\) | \(2.2728\) | \(\Gamma_0(N)\)-optimal |
| 37026.bp2 | 37026bd2 | \([1, -1, 1, -287519, 890950151]\) | \(-2035346265217/264305213568\) | \(-341341717362776203392\) | \([2]\) | \(2150400\) | \(2.6194\) |
Rank
sage: E.rank()
The elliptic curves in class 37026.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 37026.bp do not have complex multiplication.Modular form 37026.2.a.bp
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.
