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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 8470.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8470.x1 | 8470v2 | \([1, -1, 1, -961588, 363177367]\) | \(73877525106256274859/48189030400\) | \(64139599462400\) | \([2]\) | \(80640\) | \(1.9671\) | |
| 8470.x2 | 8470v1 | \([1, -1, 1, -60468, 5612951]\) | \(18370278334948779/460366807040\) | \(612748220170240\) | \([2]\) | \(40320\) | \(1.6205\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8470.x have rank \(1\).
Complex multiplication
The elliptic curves in class 8470.x do not have complex multiplication.Modular form 8470.2.a.x
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.
