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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 20800x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20800.di2 | 20800x1 | \([0, 1, 0, -13, 13]\) | \(163840/13\) | \(20800\) | \([]\) | \(1728\) | \(-0.42785\) | \(\Gamma_0(N)\)-optimal |
| 20800.di1 | 20800x2 | \([0, 1, 0, -213, -1267]\) | \(671088640/2197\) | \(3515200\) | \([]\) | \(5184\) | \(0.12146\) |
Rank
sage: E.rank()
The elliptic curves in class 20800x have rank \(0\).
Complex multiplication
The elliptic curves in class 20800x do not have complex multiplication.Modular form 20800.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
