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SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 28224.fh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28224.fh1 | 28224bv2 | \([0, 0, 0, -78204, 7798448]\) | \(109744/9\) | \(4337828094394368\) | \([2]\) | \(172032\) | \(1.7431\) | |
| 28224.fh2 | 28224bv1 | \([0, 0, 0, -16464, -672280]\) | \(16384/3\) | \(90371418633216\) | \([2]\) | \(86016\) | \(1.3965\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28224.fh have rank \(1\).
Complex multiplication
The elliptic curves in class 28224.fh do not have complex multiplication.Modular form 28224.2.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.
