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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 397800cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
397800.cu1 | 397800cu1 | \([0, 0, 0, -695068950, 7053200549125]\) | \(203769809659907949070336/2016474841511325\) | \(367502539865438981250000\) | \([2]\) | \(97320960\) | \(3.6817\) | \(\Gamma_0(N)\)-optimal |
397800.cu2 | 397800cu2 | \([0, 0, 0, -678487575, 7405704000250]\) | \(-11845731628994222232016/1269935194601506875\) | \(-3703131027457994047500000000\) | \([2]\) | \(194641920\) | \(4.0283\) |
Rank
sage: E.rank()
The elliptic curves in class 397800cu have rank \(1\).
Complex multiplication
The elliptic curves in class 397800cu do not have complex multiplication.Modular form 397800.2.a.cu
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.