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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 9792bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9792.i4 | 9792bs1 | \([0, 0, 0, -396, 1296]\) | \(35937/17\) | \(3248750592\) | \([2]\) | \(4096\) | \(0.51924\) | \(\Gamma_0(N)\)-optimal |
| 9792.i2 | 9792bs2 | \([0, 0, 0, -3276, -71280]\) | \(20346417/289\) | \(55228760064\) | \([2, 2]\) | \(8192\) | \(0.86582\) | |
| 9792.i1 | 9792bs3 | \([0, 0, 0, -52236, -4595184]\) | \(82483294977/17\) | \(3248750592\) | \([2]\) | \(16384\) | \(1.2124\) | |
| 9792.i3 | 9792bs4 | \([0, 0, 0, -396, -192240]\) | \(-35937/83521\) | \(-15961111658496\) | \([2]\) | \(16384\) | \(1.2124\) |
Rank
sage: E.rank()
The elliptic curves in class 9792bs have rank \(1\).
Complex multiplication
The elliptic curves in class 9792bs do not have complex multiplication.Modular form 9792.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
