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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 33930.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33930.j1 | 33930m4 | \([1, -1, 0, -582489, 171237645]\) | \(29981943972267024529/4007065140000\) | \(2921150487060000\) | \([2]\) | \(307200\) | \(1.9867\) | |
| 33930.j2 | 33930m3 | \([1, -1, 0, -234009, -41788467]\) | \(1943993954077461649/87266819409120\) | \(63617511349248480\) | \([2]\) | \(307200\) | \(1.9867\) | |
| 33930.j3 | 33930m2 | \([1, -1, 0, -39609, 2184813]\) | \(9427227449071249/2652468249600\) | \(1933649353958400\) | \([2, 2]\) | \(153600\) | \(1.6402\) | |
| 33930.j4 | 33930m1 | \([1, -1, 0, 6471, 221805]\) | \(41102915774831/53367275520\) | \(-38904743854080\) | \([2]\) | \(76800\) | \(1.2936\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33930.j have rank \(0\).
Complex multiplication
The elliptic curves in class 33930.j do not have complex multiplication.Modular form 33930.2.a.j
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
