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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 141570.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141570.e1 | 141570ds4 | \([1, -1, 0, -950236920, -11274151561920]\) | \(73474353581350183614361/576510977802240\) | \(744545461608462976450560\) | \([2]\) | \(49766400\) | \(3.7536\) | |
| 141570.e2 | 141570ds3 | \([1, -1, 0, -58128120, -183990225600]\) | \(-16818951115904497561/1592332281446400\) | \(-2056446137492718590361600\) | \([2]\) | \(24883200\) | \(3.4071\) | |
| 141570.e3 | 141570ds2 | \([1, -1, 0, -17426745, 1058453325]\) | \(453198971846635561/261896250564000\) | \(338230618804604184516000\) | \([2]\) | \(16588800\) | \(3.2043\) | |
| 141570.e4 | 141570ds1 | \([1, -1, 0, 4353255, 130625325]\) | \(7064514799444439/4094064000000\) | \(-5287352519036016000000\) | \([2]\) | \(8294400\) | \(2.8578\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141570.e have rank \(1\).
Complex multiplication
The elliptic curves in class 141570.e do not have complex multiplication.Modular form 141570.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
