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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 64350du
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
64350.dl1 | 64350du1 | \([1, -1, 1, -1299240230, -18044127462603]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-298561595611471594974000000\) | \([]\) | \(39513600\) | \(3.9898\) | \(\Gamma_0(N)\)-optimal |
64350.dl2 | 64350du2 | \([1, -1, 1, 3679445020, 1132461345731397]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-557215441492499634120943456968750\) | \([]\) | \(276595200\) | \(4.9628\) |
Rank
sage: E.rank()
The elliptic curves in class 64350du have rank \(0\).
Complex multiplication
The elliptic curves in class 64350du do not have complex multiplication.Modular form 64350.2.a.du
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.