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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 415794bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
415794.bj2 | 415794bj1 | \([1, 0, 0, -1129426, -439212316]\) | \(1076291879750641/60150618144\) | \(8904450230846570016\) | \([]\) | \(10626000\) | \(2.3911\) | \(\Gamma_0(N)\)-optimal* |
415794.bj1 | 415794bj2 | \([1, 0, 0, -120106816, 506629426334]\) | \(1294373635812597347281/2083292441154\) | \(308402048573212575906\) | \([]\) | \(53130000\) | \(3.1958\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 415794bj have rank \(1\).
Complex multiplication
The elliptic curves in class 415794bj do not have complex multiplication.Modular form 415794.2.a.bj
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.