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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 132600.cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
132600.cd1 | 132600k2 | \([0, 1, 0, -1308, 3888]\) | \(61918288/33813\) | \(135252000000\) | \([2]\) | \(131072\) | \(0.82665\) | |
132600.cd2 | 132600k1 | \([0, 1, 0, 317, 638]\) | \(14047232/8619\) | \(-2154750000\) | \([2]\) | \(65536\) | \(0.48008\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 132600.cd have rank \(1\).
Complex multiplication
The elliptic curves in class 132600.cd do not have complex multiplication.Modular form 132600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.