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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 98397.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98397.s1 | 98397y4 | \([1, -1, 0, -526203, 147047076]\) | \(37159393753/1053\) | \(456608389662477\) | \([2]\) | \(716800\) | \(1.9146\) | |
| 98397.s2 | 98397y3 | \([1, -1, 0, -147753, -19758546]\) | \(822656953/85683\) | \(37154393781054147\) | \([2]\) | \(716800\) | \(1.9146\) | |
| 98397.s3 | 98397y2 | \([1, -1, 0, -34218, 2108295]\) | \(10218313/1521\) | \(659545451734689\) | \([2, 2]\) | \(358400\) | \(1.5680\) | |
| 98397.s4 | 98397y1 | \([1, -1, 0, 3627, 178200]\) | \(12167/39\) | \(-16911421839351\) | \([2]\) | \(179200\) | \(1.2214\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 98397.s have rank \(1\).
Complex multiplication
The elliptic curves in class 98397.s do not have complex multiplication.Modular form 98397.2.a.s
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.
