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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 188760.ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
188760.ca1 | 188760cb2 | \([0, 1, 0, -4616, 31920]\) | \(3991233958/2132325\) | \(5812479129600\) | \([2]\) | \(430080\) | \(1.1405\) | |
188760.ca2 | 188760cb1 | \([0, 1, 0, 1104, 4464]\) | \(109083604/68445\) | \(-93286702080\) | \([2]\) | \(215040\) | \(0.79397\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 188760.ca have rank \(0\).
Complex multiplication
The elliptic curves in class 188760.ca do not have complex multiplication.Modular form 188760.2.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.