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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 397800.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 397800.ch1 | 397800ch2 | \([0, 0, 0, -7026778875, -215338548906250]\) | \(13158459661252114525066/745117393587651747\) | \(2172762319701592494252000000000\) | \([2]\) | \(415744000\) | \(4.5757\) | |
| 397800.ch2 | 397800ch1 | \([0, 0, 0, -6928363875, -221969259531250]\) | \(25226572870537521199412/88284716200629\) | \(128719116220517082000000000\) | \([2]\) | \(207872000\) | \(4.2291\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 397800.ch have rank \(0\).
Complex multiplication
The elliptic curves in class 397800.ch do not have complex multiplication.Modular form 397800.2.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.
