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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 450840z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 450840.z1 | 450840z1 | \([0, -1, 0, -81213720, 281308387932]\) | \(2396726313900986596/4154072495625\) | \(102675672570010250880000\) | \([2]\) | \(53084160\) | \(3.3094\) | \(\Gamma_0(N)\)-optimal |
| 450840.z2 | 450840z2 | \([0, -1, 0, -55816400, 460420447500]\) | \(-389032340685029858/1627263833203125\) | \(-80441739376936797600000000\) | \([2]\) | \(106168320\) | \(3.6559\) |
Rank
sage: E.rank()
The elliptic curves in class 450840z have rank \(1\).
Complex multiplication
The elliptic curves in class 450840z do not have complex multiplication.Modular form 450840.2.a.z
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.
