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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 405600.cx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 405600.cx1 | 405600cx1 | \([0, -1, 0, -12262358, -16518613788]\) | \(42246001231552/14414517\) | \(69576120386253000000\) | \([2]\) | \(16515072\) | \(2.7790\) | \(\Gamma_0(N)\)-optimal |
| 405600.cx2 | 405600cx2 | \([0, -1, 0, -10551233, -21294363663]\) | \(-420526439488/390971529\) | \(-120777273274941504000000\) | \([2]\) | \(33030144\) | \(3.1256\) |
Rank
sage: E.rank()
The elliptic curves in class 405600.cx have rank \(1\).
Complex multiplication
The elliptic curves in class 405600.cx do not have complex multiplication.Modular form 405600.2.a.cx
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.
