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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 166410bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 166410.r2 | 166410bl1 | \([1, -1, 0, -70766199, -70817407907]\) | \(106968940723/55987200\) | \(20513150997529173562598400\) | \([2]\) | \(50856960\) | \(3.5487\) | \(\Gamma_0(N)\)-optimal |
| 166410.r1 | 166410bl2 | \([1, -1, 0, -643216599, 6227167402813]\) | \(80325199737523/765275040\) | \(280389132697476891133766880\) | \([2]\) | \(101713920\) | \(3.8953\) |
Rank
sage: E.rank()
The elliptic curves in class 166410bl have rank \(1\).
Complex multiplication
The elliptic curves in class 166410bl do not have complex multiplication.Modular form 166410.2.a.bl
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.
