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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 227700.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 227700.ch1 | 227700by2 | \([0, 0, 0, -51375, -2902250]\) | \(5142706000/1728243\) | \(5039556588000000\) | \([2]\) | \(1327104\) | \(1.7154\) | |
| 227700.ch2 | 227700by1 | \([0, 0, 0, -21000, 1137625]\) | \(5619712000/184437\) | \(33613643250000\) | \([2]\) | \(663552\) | \(1.3689\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 227700.ch have rank \(1\).
Complex multiplication
The elliptic curves in class 227700.ch do not have complex multiplication.Modular form 227700.2.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 LMFDB 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 LMFDB labels.
