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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 6288d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6288.d2 | 6288d1 | \([0, -1, 0, -34160, -2298432]\) | \(1076291879750641/60150618144\) | \(246376931917824\) | \([]\) | \(20160\) | \(1.5165\) | \(\Gamma_0(N)\)-optimal |
6288.d1 | 6288d2 | \([0, -1, 0, -3632720, 2666200128]\) | \(1294373635812597347281/2083292441154\) | \(8533165838966784\) | \([]\) | \(100800\) | \(2.3212\) |
Rank
sage: E.rank()
The elliptic curves in class 6288d have rank \(0\).
Complex multiplication
The elliptic curves in class 6288d do not have complex multiplication.Modular form 6288.2.a.d
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.