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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 17600di
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17600.n2 | 17600di1 | \([0, 1, 0, -353, -4577]\) | \(-148877/176\) | \(-5767168000\) | \([2]\) | \(9216\) | \(0.56690\) | \(\Gamma_0(N)\)-optimal |
17600.n1 | 17600di2 | \([0, 1, 0, -6753, -215777]\) | \(1039509197/484\) | \(15859712000\) | \([2]\) | \(18432\) | \(0.91347\) |
Rank
sage: E.rank()
The elliptic curves in class 17600di have rank \(0\).
Complex multiplication
The elliptic curves in class 17600di do not have complex multiplication.Modular form 17600.2.a.di
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.