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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 51600.df
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51600.df1 | 51600de2 | \([0, 1, 0, -23960408, 45140263188]\) | \(-23769846831649063249/3261823333284\) | \(-208756693330176000000\) | \([]\) | \(3951360\) | \(2.9168\) | |
51600.df2 | 51600de1 | \([0, 1, 0, 63592, -13768812]\) | \(444369620591/1540767744\) | \(-98609135616000000\) | \([]\) | \(564480\) | \(1.9438\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 51600.df have rank \(0\).
Complex multiplication
The elliptic curves in class 51600.df do not have complex multiplication.Modular form 51600.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.