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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 235200.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.dn1 | 235200dn1 | \([0, -1, 0, -26133, -588363]\) | \(1048576/525\) | \(988251600000000\) | \([2]\) | \(884736\) | \(1.5700\) | \(\Gamma_0(N)\)-optimal |
| 235200.dn2 | 235200dn2 | \([0, -1, 0, 96367, -4630863]\) | \(3286064/2205\) | \(-66410507520000000\) | \([2]\) | \(1769472\) | \(1.9166\) |
Rank
sage: E.rank()
The elliptic curves in class 235200.dn have rank \(2\).
Complex multiplication
The elliptic curves in class 235200.dn do not have complex multiplication.Modular form 235200.2.a.dn
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.
