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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 208208b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 208208.d2 | 208208b1 | \([0, 1, 0, -39264, 3083380]\) | \(-338608873/13552\) | \(-267931302166528\) | \([2]\) | \(829440\) | \(1.5367\) | \(\Gamma_0(N)\)-optimal |
| 208208.d1 | 208208b2 | \([0, 1, 0, -634144, 194158836]\) | \(1426487591593/2156\) | \(42625434435584\) | \([2]\) | \(1658880\) | \(1.8833\) |
Rank
sage: E.rank()
The elliptic curves in class 208208b have rank \(1\).
Complex multiplication
The elliptic curves in class 208208b do not have complex multiplication.Modular form 208208.2.a.b
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.
