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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 206400.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206400.l1 | 206400iz1 | \([0, -1, 0, -36033, 2591937]\) | \(1263214441/29025\) | \(118886400000000\) | \([2]\) | \(884736\) | \(1.4871\) | \(\Gamma_0(N)\)-optimal |
| 206400.l2 | 206400iz2 | \([0, -1, 0, 3967, 7991937]\) | \(1685159/6739605\) | \(-27605422080000000\) | \([2]\) | \(1769472\) | \(1.8337\) |
Rank
sage: E.rank()
The elliptic curves in class 206400.l have rank \(1\).
Complex multiplication
The elliptic curves in class 206400.l do not have complex multiplication.Modular form 206400.2.a.l
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.
