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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 2450.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2450.ba1 | 2450bb2 | \([1, -1, 1, -8363305, 9311358697]\) | \(-5745702166029/8192\) | \(-92236816000000000\) | \([]\) | \(65520\) | \(2.5267\) | |
| 2450.ba2 | 2450bb1 | \([1, -1, 1, -2680, -233803]\) | \(-189/2\) | \(-22518753906250\) | \([]\) | \(5040\) | \(1.2442\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2450.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 2450.ba do not have complex multiplication.Modular form 2450.2.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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
