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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 89232ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 89232.cb2 | 89232ch1 | \([0, 1, 0, 5352, -188460]\) | \(857375/1287\) | \(-25444774637568\) | \([2]\) | \(172032\) | \(1.2577\) | \(\Gamma_0(N)\)-optimal |
| 89232.cb1 | 89232ch2 | \([0, 1, 0, -35208, -1924428]\) | \(244140625/61347\) | \(1212867591057408\) | \([2]\) | \(344064\) | \(1.6043\) |
Rank
sage: E.rank()
The elliptic curves in class 89232ch have rank \(0\).
Complex multiplication
The elliptic curves in class 89232ch do not have complex multiplication.Modular form 89232.2.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.
