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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 2550v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2550.u2 | 2550v1 | \([1, 1, 1, -6388, 193781]\) | \(1845026709625/793152\) | \(12393000000\) | \([2]\) | \(3456\) | \(0.89684\) | \(\Gamma_0(N)\)-optimal |
| 2550.u3 | 2550v2 | \([1, 1, 1, -5388, 257781]\) | \(-1107111813625/1228691592\) | \(-19198306125000\) | \([2]\) | \(6912\) | \(1.2434\) | |
| 2550.u1 | 2550v3 | \([1, 1, 1, -18763, -755719]\) | \(46753267515625/11591221248\) | \(181112832000000\) | \([2]\) | \(10368\) | \(1.4461\) | |
| 2550.u4 | 2550v4 | \([1, 1, 1, 45237, -4723719]\) | \(655215969476375/1001033261568\) | \(-15641144712000000\) | \([2]\) | \(20736\) | \(1.7927\) |
Rank
sage: E.rank()
The elliptic curves in class 2550v have rank \(1\).
Complex multiplication
The elliptic curves in class 2550v do not have complex multiplication.Modular form 2550.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
