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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 19890.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19890.s1 | 19890t3 | \([1, -1, 1, -66578, 6587331]\) | \(44769506062996441/323730468750\) | \(235999511718750\) | \([2]\) | \(172032\) | \(1.5896\) | |
| 19890.s2 | 19890t2 | \([1, -1, 1, -6908, -47973]\) | \(50002789171321/27473062500\) | \(20027862562500\) | \([2, 2]\) | \(86016\) | \(1.2430\) | |
| 19890.s3 | 19890t1 | \([1, -1, 1, -5288, -146469]\) | \(22428153804601/35802000\) | \(26099658000\) | \([2]\) | \(43008\) | \(0.89642\) | \(\Gamma_0(N)\)-optimal |
| 19890.s4 | 19890t4 | \([1, -1, 1, 26842, -398973]\) | \(2933972022568679/1789082460750\) | \(-1304241113886750\) | \([2]\) | \(172032\) | \(1.5896\) |
Rank
sage: E.rank()
The elliptic curves in class 19890.s have rank \(0\).
Complex multiplication
The elliptic curves in class 19890.s do not have complex multiplication.Modular form 19890.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
