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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 9800.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9800.d1 | 9800u2 | \([0, 1, 0, -34708, -2472912]\) | \(78608\) | \(58824500000000\) | \([2]\) | \(28800\) | \(1.4510\) | |
9800.d2 | 9800u1 | \([0, 1, 0, -4083, 38338]\) | \(2048\) | \(3676531250000\) | \([2]\) | \(14400\) | \(1.1045\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9800.d have rank \(1\).
Complex multiplication
The elliptic curves in class 9800.d do not have complex multiplication.Modular form 9800.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.