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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 16337.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16337.a1 | 16337a3 | \([1, -1, 1, -87151, 9924502]\) | \(82483294977/17\) | \(15087562577\) | \([2]\) | \(30240\) | \(1.3404\) | |
| 16337.a2 | 16337a2 | \([1, -1, 1, -5466, 154976]\) | \(20346417/289\) | \(256488563809\) | \([2, 2]\) | \(15120\) | \(0.99378\) | |
| 16337.a3 | 16337a1 | \([1, -1, 1, -661, -2628]\) | \(35937/17\) | \(15087562577\) | \([2]\) | \(7560\) | \(0.64721\) | \(\Gamma_0(N)\)-optimal |
| 16337.a4 | 16337a4 | \([1, -1, 1, -661, 414446]\) | \(-35937/83521\) | \(-74125194940801\) | \([2]\) | \(30240\) | \(1.3404\) |
Rank
sage: E.rank()
The elliptic curves in class 16337.a have rank \(0\).
Complex multiplication
The elliptic curves in class 16337.a do not have complex multiplication.Modular form 16337.2.a.a
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.
