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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 235950.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235950.bb1 | 235950bb4 | \([1, 1, 0, -79870650, -274777724250]\) | \(2035678735521204409/141376950\) | \(3913404545608593750\) | \([2]\) | \(17694720\) | \(3.0217\) | |
| 235950.bb2 | 235950bb3 | \([1, 1, 0, -8541150, 2557361250]\) | \(2489411558640889/1338278906250\) | \(37044417459924316406250\) | \([2]\) | \(17694720\) | \(3.0217\) | |
| 235950.bb3 | 235950bb2 | \([1, 1, 0, -5001900, -4276930500]\) | \(499980107400409/4140922500\) | \(114623387578476562500\) | \([2, 2]\) | \(8847360\) | \(2.6751\) | |
| 235950.bb4 | 235950bb1 | \([1, 1, 0, -101400, -155610000]\) | \(-4165509529/375289200\) | \(-10388245475643750000\) | \([2]\) | \(4423680\) | \(2.3285\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235950.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 235950.bb do not have complex multiplication.Modular form 235950.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
