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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 381150ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 381150.ba1 | 381150ba1 | \([1, -1, 0, -699342, 84823316]\) | \(69426531/34496\) | \(18794733352857000000\) | \([2]\) | \(8847360\) | \(2.3913\) | \(\Gamma_0(N)\)-optimal |
| 381150.ba2 | 381150ba2 | \([1, -1, 0, 2567658, 650014316]\) | \(3436115229/2324168\) | \(-1266295159648740375000\) | \([2]\) | \(17694720\) | \(2.7379\) |
Rank
sage: E.rank()
The elliptic curves in class 381150ba have rank \(0\).
Complex multiplication
The elliptic curves in class 381150ba do not have complex multiplication.Modular form 381150.2.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 Cremona 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 Cremona labels.
