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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 257600.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257600.dn1 | 257600dn2 | \([0, 0, 0, -97900, 11790000]\) | \(50668941906/1127\) | \(2308096000000\) | \([2]\) | \(524288\) | \(1.4872\) | |
| 257600.dn2 | 257600dn1 | \([0, 0, 0, -5900, 198000]\) | \(-22180932/3703\) | \(-3791872000000\) | \([2]\) | \(262144\) | \(1.1407\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 257600.dn have rank \(1\).
Complex multiplication
The elliptic curves in class 257600.dn do not have complex multiplication.Modular form 257600.2.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.
