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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 254.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254.d1 | 254d4 | \([1, -1, 1, -5419, 154883]\) | \(17595678939932673/1016\) | \(1016\) | \([2]\) | \(96\) | \(0.48968\) | |
| 254.d2 | 254d3 | \([1, -1, 1, -379, 1891]\) | \(6005741311233/2081157128\) | \(2081157128\) | \([2]\) | \(96\) | \(0.48968\) | |
| 254.d3 | 254d2 | \([1, -1, 1, -339, 2483]\) | \(4296563326593/1032256\) | \(1032256\) | \([2, 2]\) | \(48\) | \(0.14311\) | |
| 254.d4 | 254d1 | \([1, -1, 1, -19, 51]\) | \(-721734273/520192\) | \(-520192\) | \([4]\) | \(24\) | \(-0.20346\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254.d have rank \(0\).
Complex multiplication
The elliptic curves in class 254.d do not have complex multiplication.Modular form 254.2.a.d
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.
