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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 60840bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60840.bn5 | 60840bs1 | \([0, 0, 0, -23322, -1368731]\) | \(24918016/45\) | \(2533495507920\) | \([2]\) | \(122880\) | \(1.2721\) | \(\Gamma_0(N)\)-optimal |
| 60840.bn4 | 60840bs2 | \([0, 0, 0, -30927, -399854]\) | \(3631696/2025\) | \(1824116765702400\) | \([2, 2]\) | \(245760\) | \(1.6186\) | |
| 60840.bn6 | 60840bs3 | \([0, 0, 0, 121173, -3168074]\) | \(54607676/32805\) | \(-118202766417515520\) | \([2]\) | \(491520\) | \(1.9652\) | |
| 60840.bn2 | 60840bs4 | \([0, 0, 0, -304707, 64376494]\) | \(868327204/5625\) | \(20267964063360000\) | \([2, 2]\) | \(491520\) | \(1.9652\) | |
| 60840.bn3 | 60840bs5 | \([0, 0, 0, -122187, 140779366]\) | \(-27995042/1171875\) | \(-8444985026400000000\) | \([2]\) | \(983040\) | \(2.3118\) | |
| 60840.bn1 | 60840bs6 | \([0, 0, 0, -4867707, 4133659894]\) | \(1770025017602/75\) | \(540479041689600\) | \([2]\) | \(983040\) | \(2.3118\) |
Rank
sage: E.rank()
The elliptic curves in class 60840bs have rank \(0\).
Complex multiplication
The elliptic curves in class 60840bs do not have complex multiplication.Modular form 60840.2.a.bs
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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
