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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 8400.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8400.ca1 | 8400cm1 | \([0, 1, 0, -68208, -6842412]\) | \(4386781853/27216\) | \(217728000000000\) | \([2]\) | \(38400\) | \(1.5892\) | \(\Gamma_0(N)\)-optimal |
| 8400.ca2 | 8400cm2 | \([0, 1, 0, -28208, -14762412]\) | \(-310288733/11573604\) | \(-92588832000000000\) | \([2]\) | \(76800\) | \(1.9358\) |
Rank
sage: E.rank()
The elliptic curves in class 8400.ca have rank \(0\).
Complex multiplication
The elliptic curves in class 8400.ca do not have complex multiplication.Modular form 8400.2.a.ca
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.
