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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 80400df
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
80400.dk2 | 80400df1 | \([0, 1, 0, 95467, -1693437]\) | \(1503484706816/890163675\) | \(-56970475200000000\) | \([]\) | \(829440\) | \(1.9045\) | \(\Gamma_0(N)\)-optimal |
80400.dk1 | 80400df2 | \([0, 1, 0, -1200533, 558826563]\) | \(-2989967081734144/380653171875\) | \(-24361803000000000000\) | \([]\) | \(2488320\) | \(2.4538\) |
Rank
sage: E.rank()
The elliptic curves in class 80400df have rank \(0\).
Complex multiplication
The elliptic curves in class 80400df do not have complex multiplication.Modular form 80400.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.