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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 28224.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28224.u1 | 28224co2 | \([0, 0, 0, -20081964, -34815229904]\) | \(-16591834777/98304\) | \(-5306632837225613623296\) | \([]\) | \(1935360\) | \(3.0089\) | |
| 28224.u2 | 28224co1 | \([0, 0, 0, 662676, -254659664]\) | \(596183/864\) | \(-46640327670928244736\) | \([]\) | \(645120\) | \(2.4596\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28224.u have rank \(1\).
Complex multiplication
The elliptic curves in class 28224.u do not have complex multiplication.Modular form 28224.2.a.u
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
