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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 134640bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 134640.g4 | 134640bs1 | \([0, 0, 0, 1077, -90502]\) | \(46268279/1211760\) | \(-3618295971840\) | \([2]\) | \(196608\) | \(1.0899\) | \(\Gamma_0(N)\)-optimal |
| 134640.g3 | 134640bs2 | \([0, 0, 0, -24843, -1433158]\) | \(567869252041/31472100\) | \(93975187046400\) | \([2, 2]\) | \(393216\) | \(1.4365\) | |
| 134640.g2 | 134640bs3 | \([0, 0, 0, -72363, 5685338]\) | \(14034143923561/3445241250\) | \(10287435248640000\) | \([2]\) | \(786432\) | \(1.7830\) | |
| 134640.g1 | 134640bs4 | \([0, 0, 0, -392043, -94481638]\) | \(2231707882611241/7466910\) | \(22296073789440\) | \([2]\) | \(786432\) | \(1.7830\) |
Rank
sage: E.rank()
The elliptic curves in class 134640bs have rank \(1\).
Complex multiplication
The elliptic curves in class 134640bs do not have complex multiplication.Modular form 134640.2.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.
