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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 228800.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 228800.ba1 | 228800r2 | \([0, 1, 0, -3548033, -2573527937]\) | \(1205943158724121/1258400\) | \(5154406400000000\) | \([2]\) | \(4423680\) | \(2.3047\) | |
| 228800.ba2 | 228800r1 | \([0, 1, 0, -220033, -40919937]\) | \(-287626699801/9518080\) | \(-38986055680000000\) | \([2]\) | \(2211840\) | \(1.9582\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 228800.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 228800.ba do not have complex multiplication.Modular form 228800.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
