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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 236992.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 236992.bp1 | 236992bp3 | \([0, 0, 0, -632684, 193698640]\) | \(1443468546/7\) | \(135823520301056\) | \([2]\) | \(1622016\) | \(1.9123\) | |
| 236992.bp2 | 236992bp4 | \([0, 0, 0, -124844, -13432368]\) | \(11090466/2401\) | \(46587467463262208\) | \([2]\) | \(1622016\) | \(1.9123\) | |
| 236992.bp3 | 236992bp2 | \([0, 0, 0, -40204, 2920080]\) | \(740772/49\) | \(475382321053696\) | \([2, 2]\) | \(811008\) | \(1.5657\) | |
| 236992.bp4 | 236992bp1 | \([0, 0, 0, 2116, 194672]\) | \(432/7\) | \(-16977940037632\) | \([2]\) | \(405504\) | \(1.2191\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 236992.bp have rank \(1\).
Complex multiplication
The elliptic curves in class 236992.bp do not have complex multiplication.Modular form 236992.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
