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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 274890.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 274890.bp1 | 274890bp4 | \([1, 1, 0, -10797812, 13547799336]\) | \(1183430669265454849849/10449720703125000\) | \(1229399191001953125000\) | \([2]\) | \(24883200\) | \(2.8702\) | |
| 274890.bp2 | 274890bp3 | \([1, 1, 0, -1168332, -139543536]\) | \(1499114720492202169/796539777000000\) | \(93712108224273000000\) | \([2]\) | \(12441600\) | \(2.5236\) | |
| 274890.bp3 | 274890bp2 | \([1, 1, 0, -926027, -332303901]\) | \(746461053445307689/27443694341250\) | \(3228723195553721250\) | \([2]\) | \(8294400\) | \(2.3209\) | |
| 274890.bp4 | 274890bp1 | \([1, 1, 0, -917697, -338756319]\) | \(726497538898787209/1038579300\) | \(122187816065700\) | \([2]\) | \(4147200\) | \(1.9743\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 274890.bp have rank \(1\).
Complex multiplication
The elliptic curves in class 274890.bp do not have complex multiplication.Modular form 274890.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
