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SageMath
E = EllipticCurve("fj1")
E.isogeny_class()
Elliptic curves in class 101430.fj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101430.fj1 | 101430ey4 | \([1, -1, 1, -216955472, -698990090781]\) | \(13167998447866683762601/5158996582031250000\) | \(442467125093078613281250000\) | \([2]\) | \(47185920\) | \(3.8115\) | |
| 101430.fj2 | 101430ey2 | \([1, -1, 1, -97673792, 363857390691]\) | \(1201550658189465626281/28577902500000000\) | \(2451015843741202500000000\) | \([2, 2]\) | \(23592960\) | \(3.4649\) | |
| 101430.fj3 | 101430ey1 | \([1, -1, 1, -97109312, 368356070499]\) | \(1180838681727016392361/692428800000\) | \(59386932244684800000\) | \([2]\) | \(11796480\) | \(3.1184\) | \(\Gamma_0(N)\)-optimal |
| 101430.fj4 | 101430ey3 | \([1, -1, 1, 12576208, 1138782590691]\) | \(2564821295690373719/6533572090396050000\) | \(-560359134467130562222050000\) | \([2]\) | \(47185920\) | \(3.8115\) |
Rank
sage: E.rank()
The elliptic curves in class 101430.fj have rank \(1\).
Complex multiplication
The elliptic curves in class 101430.fj do not have complex multiplication.Modular form 101430.2.a.fj
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.
