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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 235200.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.bs1 | 235200bs3 | \([0, -1, 0, -276033, 55403937]\) | \(38614472/405\) | \(24395696640000000\) | \([2]\) | \(2359296\) | \(1.9610\) | |
| 235200.bs2 | 235200bs2 | \([0, -1, 0, -31033, -701063]\) | \(438976/225\) | \(1694145600000000\) | \([2, 2]\) | \(1179648\) | \(1.6144\) | |
| 235200.bs3 | 235200bs1 | \([0, -1, 0, -24908, -1503438]\) | \(14526784/15\) | \(1764735000000\) | \([2]\) | \(589824\) | \(1.2678\) | \(\Gamma_0(N)\)-optimal |
| 235200.bs4 | 235200bs4 | \([0, -1, 0, 115967, -5552063]\) | \(2863288/1875\) | \(-112943040000000000\) | \([2]\) | \(2359296\) | \(1.9610\) |
Rank
sage: E.rank()
The elliptic curves in class 235200.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 235200.bs do not have complex multiplication.Modular form 235200.2.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 LMFDB 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 LMFDB labels.
