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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 466752.cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466752.cb1 | 466752cb1 | \([0, -1, 0, -2525281, 1323593953]\) | \(6793805286030262681/1048227429629952\) | \(274786531312914137088\) | \([2]\) | \(28901376\) | \(2.6453\) | \(\Gamma_0(N)\)-optimal |
466752.cb2 | 466752cb2 | \([0, -1, 0, 4396959, 7297487073]\) | \(35862531227445945959/108547797844556928\) | \(-28455153918163531333632\) | \([2]\) | \(57802752\) | \(2.9919\) |
Rank
sage: E.rank()
The elliptic curves in class 466752.cb have rank \(0\).
Complex multiplication
The elliptic curves in class 466752.cb do not have complex multiplication.Modular form 466752.2.a.cb
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.