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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 93600.dn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93600.dn1 | 93600ee1 | \([0, 0, 0, -653025, -203055500]\) | \(42246001231552/14414517\) | \(10508182893000000\) | \([2]\) | \(786432\) | \(2.0458\) | \(\Gamma_0(N)\)-optimal |
93600.dn2 | 93600ee2 | \([0, 0, 0, -561900, -261740000]\) | \(-420526439488/390971529\) | \(-18241167657024000000\) | \([2]\) | \(1572864\) | \(2.3924\) |
Rank
sage: E.rank()
The elliptic curves in class 93600.dn have rank \(0\).
Complex multiplication
The elliptic curves in class 93600.dn do not have complex multiplication.Modular form 93600.2.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.