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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 258.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 258.d1 | 258d3 | \([1, 1, 1, -5504, -159463]\) | \(18440127492397057/1032\) | \(1032\) | \([2]\) | \(240\) | \(0.49308\) | |
| 258.d2 | 258d2 | \([1, 1, 1, -344, -2599]\) | \(4502751117697/1065024\) | \(1065024\) | \([2, 2]\) | \(120\) | \(0.14650\) | |
| 258.d3 | 258d4 | \([1, 1, 1, -304, -3175]\) | \(-3107661785857/2215383048\) | \(-2215383048\) | \([2]\) | \(240\) | \(0.49308\) | |
| 258.d4 | 258d1 | \([1, 1, 1, -24, -39]\) | \(1532808577/528384\) | \(528384\) | \([4]\) | \(60\) | \(-0.20007\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 258.d have rank \(0\).
Complex multiplication
The elliptic curves in class 258.d do not have complex multiplication.Modular form 258.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
