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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 221067ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221067.ba2 | 221067ba1 | \([1, -1, 0, -445968, -93232661]\) | \(5706550403/1112643\) | \(1912570860720081177\) | \([2]\) | \(2433024\) | \(2.2247\) | \(\Gamma_0(N)\)-optimal |
| 221067.ba1 | 221067ba2 | \([1, -1, 0, -2182923, 1157722330]\) | \(669233048723/50759541\) | \(87252801680436806799\) | \([2]\) | \(4866048\) | \(2.5713\) |
Rank
sage: E.rank()
The elliptic curves in class 221067ba have rank \(0\).
Complex multiplication
The elliptic curves in class 221067ba do not have complex multiplication.Modular form 221067.2.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.
