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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 3920.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3920.ba1 | 3920bc3 | \([0, 1, 0, -102965, -13337437]\) | \(-250523582464/13671875\) | \(-6588344000000000\) | \([]\) | \(20736\) | \(1.7936\) | |
| 3920.ba2 | 3920bc1 | \([0, 1, 0, -1045, 14083]\) | \(-262144/35\) | \(-16866160640\) | \([]\) | \(2304\) | \(0.69495\) | \(\Gamma_0(N)\)-optimal |
| 3920.ba3 | 3920bc2 | \([0, 1, 0, 6795, -34525]\) | \(71991296/42875\) | \(-20661046784000\) | \([]\) | \(6912\) | \(1.2443\) |
Rank
sage: E.rank()
The elliptic curves in class 3920.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 3920.ba do not have complex multiplication.Modular form 3920.2.a.ba
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
