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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 208208h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 208208.k2 | 208208h1 | \([0, 1, 0, 9408, -1329548]\) | \(4657463/41503\) | \(-820539612884992\) | \([2]\) | \(829440\) | \(1.5430\) | \(\Gamma_0(N)\)-optimal |
| 208208.k1 | 208208h2 | \([0, 1, 0, -139312, -18521580]\) | \(15124197817/1294139\) | \(25585917019959296\) | \([2]\) | \(1658880\) | \(1.8896\) |
Rank
sage: E.rank()
The elliptic curves in class 208208h have rank \(1\).
Complex multiplication
The elliptic curves in class 208208h do not have complex multiplication.Modular form 208208.2.a.h
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.
