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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 194271.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 194271.h1 | 194271e4 | \([1, 0, 0, -1050847, -414442990]\) | \(215751695207833/163381911\) | \(97183370892346431\) | \([2]\) | \(2795520\) | \(2.1923\) | |
| 194271.h2 | 194271e2 | \([1, 0, 0, -79492, -3559825]\) | \(93391282153/44876601\) | \(26693648842011921\) | \([2, 2]\) | \(1397760\) | \(1.8457\) | |
| 194271.h3 | 194271e1 | \([1, 0, 0, -41647, 3229568]\) | \(13430356633/180873\) | \(107587478539233\) | \([4]\) | \(698880\) | \(1.4991\) | \(\Gamma_0(N)\)-optimal |
| 194271.h4 | 194271e3 | \([1, 0, 0, 286343, -27046432]\) | \(4365111505607/3058314567\) | \(-1819156827405617007\) | \([2]\) | \(2795520\) | \(2.1923\) |
Rank
sage: E.rank()
The elliptic curves in class 194271.h have rank \(0\).
Complex multiplication
The elliptic curves in class 194271.h do not have complex multiplication.Modular form 194271.2.a.h
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.
