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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 32490.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32490.bk1 | 32490bo4 | \([1, -1, 1, -1600067588, 24635572389587]\) | \(13209596798923694545921/92340\) | \(3166933938972660\) | \([2]\) | \(11059200\) | \(3.5090\) | |
| 32490.bk2 | 32490bo3 | \([1, -1, 1, -101238908, 374957523731]\) | \(3345930611358906241/165622259047500\) | \(5680255070682796735327500\) | \([2]\) | \(11059200\) | \(3.5090\) | |
| 32490.bk3 | 32490bo2 | \([1, -1, 1, -100004288, 384949056467]\) | \(3225005357698077121/8526675600\) | \(292434679924735424400\) | \([2, 2]\) | \(5529600\) | \(3.1624\) | |
| 32490.bk4 | 32490bo1 | \([1, -1, 1, -6173168, 6171591251]\) | \(-758575480593601/40535043840\) | \(-1390207992794462396160\) | \([2]\) | \(2764800\) | \(2.8159\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32490.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 32490.bk do not have complex multiplication.Modular form 32490.2.a.bk
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.
