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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 34650df
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
34650.do2 | 34650df1 | \([1, -1, 1, -91130, -16514503]\) | \(-7347774183121/6119866368\) | \(-69709102848000000\) | \([2]\) | \(430080\) | \(1.9298\) | \(\Gamma_0(N)\)-optimal |
34650.do1 | 34650df2 | \([1, -1, 1, -1675130, -833858503]\) | \(45637459887836881/13417633152\) | \(152835227622000000\) | \([2]\) | \(860160\) | \(2.2764\) |
Rank
sage: E.rank()
The elliptic curves in class 34650df have rank \(0\).
Complex multiplication
The elliptic curves in class 34650df do not have complex multiplication.Modular form 34650.2.a.df
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.