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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 7488bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7488.by4 | 7488bs1 | \([0, 0, 0, 276, -3760]\) | \(12167/39\) | \(-7453016064\) | \([2]\) | \(4096\) | \(0.57751\) | \(\Gamma_0(N)\)-optimal |
| 7488.by3 | 7488bs2 | \([0, 0, 0, -2604, -44080]\) | \(10218313/1521\) | \(290667626496\) | \([2, 2]\) | \(8192\) | \(0.92409\) | |
| 7488.by1 | 7488bs3 | \([0, 0, 0, -40044, -3084208]\) | \(37159393753/1053\) | \(201231433728\) | \([2]\) | \(16384\) | \(1.2707\) | |
| 7488.by2 | 7488bs4 | \([0, 0, 0, -11244, 415568]\) | \(822656953/85683\) | \(16374276292608\) | \([2]\) | \(16384\) | \(1.2707\) |
Rank
sage: E.rank()
The elliptic curves in class 7488bs have rank \(1\).
Complex multiplication
The elliptic curves in class 7488bs do not have complex multiplication.Modular form 7488.2.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.
