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SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 81600.fh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81600.fh1 | 81600fb1 | \([0, 1, 0, -32573, 2251683]\) | \(29860725364736/3581577\) | \(458441856000\) | \([2]\) | \(239616\) | \(1.2624\) | \(\Gamma_0(N)\)-optimal |
| 81600.fh2 | 81600fb2 | \([0, 1, 0, -29873, 2643183]\) | \(-1439609866256/651714363\) | \(-1334711015424000\) | \([2]\) | \(479232\) | \(1.6089\) |
Rank
sage: E.rank()
The elliptic curves in class 81600.fh have rank \(2\).
Complex multiplication
The elliptic curves in class 81600.fh do not have complex multiplication.Modular form 81600.2.a.fh
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
