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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 188760.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 188760.e1 | 188760cl4 | \([0, -1, 0, -1473336, -273185460]\) | \(97486245727778/47497539375\) | \(172328526546359040000\) | \([2]\) | \(8110080\) | \(2.5764\) | |
| 188760.e2 | 188760cl2 | \([0, -1, 0, -781216, 263069116]\) | \(29065753681636/372683025\) | \(676076249550873600\) | \([2, 2]\) | \(4055040\) | \(2.2298\) | |
| 188760.e3 | 188760cl1 | \([0, -1, 0, -778796, 264795060]\) | \(115185902730064/19305\) | \(8755196186880\) | \([2]\) | \(2027520\) | \(1.8833\) | \(\Gamma_0(N)\)-optimal |
| 188760.e4 | 188760cl3 | \([0, -1, 0, -127816, 688824556]\) | \(-63649751618/56451816135\) | \(-204816047808382433280\) | \([2]\) | \(8110080\) | \(2.5764\) |
Rank
sage: E.rank()
The elliptic curves in class 188760.e have rank \(1\).
Complex multiplication
The elliptic curves in class 188760.e do not have complex multiplication.Modular form 188760.2.a.e
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.
