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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 188760.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 188760.b1 | 188760bd4 | \([0, -1, 0, -4266016, -3389971220]\) | \(2366492816943218/23562825\) | \(85489626767001600\) | \([2]\) | \(4915200\) | \(2.4086\) | |
| 188760.b2 | 188760bd3 | \([0, -1, 0, -965136, 308845836]\) | \(27403349188178/4524609375\) | \(16415992850400000000\) | \([2]\) | \(4915200\) | \(2.4086\) | |
| 188760.b3 | 188760bd2 | \([0, -1, 0, -273016, -50226020]\) | \(1240605018436/115025625\) | \(208665509120640000\) | \([2, 2]\) | \(2457600\) | \(2.0620\) | |
| 188760.b4 | 188760bd1 | \([0, -1, 0, 19804, -3726204]\) | \(1893932336/14274975\) | \(-6473981180409600\) | \([2]\) | \(1228800\) | \(1.7154\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 188760.b have rank \(1\).
Complex multiplication
The elliptic curves in class 188760.b do not have complex multiplication.Modular form 188760.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
