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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 96600.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96600.bk1 | 96600p4 | \([0, -1, 0, -4294008, 3426288012]\) | \(273629163383866082/26408025\) | \(845056800000000\) | \([2]\) | \(1966080\) | \(2.2980\) | |
| 96600.bk2 | 96600p3 | \([0, -1, 0, -476008, -39811988]\) | \(372749784765122/194143359375\) | \(6212587500000000000\) | \([2]\) | \(1966080\) | \(2.2980\) | |
| 96600.bk3 | 96600p2 | \([0, -1, 0, -269008, 53338012]\) | \(134555337776164/1312250625\) | \(20996010000000000\) | \([2, 2]\) | \(983040\) | \(1.9514\) | |
| 96600.bk4 | 96600p1 | \([0, -1, 0, -4508, 2025012]\) | \(-2533446736/440749575\) | \(-1762998300000000\) | \([2]\) | \(491520\) | \(1.6048\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 96600.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 96600.bk do not have complex multiplication.Modular form 96600.2.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.
