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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 48400.cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48400.cd1 | 48400k4 | \([0, 0, 0, -323675, -70875750]\) | \(132304644/5\) | \(141724880000000\) | \([2]\) | \(245760\) | \(1.8015\) | |
48400.cd2 | 48400k2 | \([0, 0, 0, -21175, -998250]\) | \(148176/25\) | \(177156100000000\) | \([2, 2]\) | \(122880\) | \(1.4549\) | |
48400.cd3 | 48400k1 | \([0, 0, 0, -6050, 166375]\) | \(55296/5\) | \(2214451250000\) | \([2]\) | \(61440\) | \(1.1083\) | \(\Gamma_0(N)\)-optimal |
48400.cd4 | 48400k3 | \([0, 0, 0, 39325, -5656750]\) | \(237276/625\) | \(-17715610000000000\) | \([2]\) | \(245760\) | \(1.8015\) |
Rank
sage: E.rank()
The elliptic curves in class 48400.cd have rank \(0\).
Complex multiplication
The elliptic curves in class 48400.cd do not have complex multiplication.Modular form 48400.2.a.cd
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.