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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 204624ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 204624.ek2 | 204624ch1 | \([0, 0, 0, -67179, -7050022]\) | \(-95443993/5887\) | \(-2068091512123392\) | \([2]\) | \(884736\) | \(1.6932\) | \(\Gamma_0(N)\)-optimal |
| 204624.ek1 | 204624ch2 | \([0, 0, 0, -1090299, -438192790]\) | \(408023180713/1421\) | \(499194502926336\) | \([2]\) | \(1769472\) | \(2.0398\) |
Rank
sage: E.rank()
The elliptic curves in class 204624ch have rank \(1\).
Complex multiplication
The elliptic curves in class 204624ch do not have complex multiplication.Modular form 204624.2.a.ch
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.
