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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 15680.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15680.bu1 | 15680bg2 | \([0, -1, 0, -101985, -13572383]\) | \(-77626969/8000\) | \(-12089663946752000\) | \([]\) | \(96768\) | \(1.8254\) | |
15680.bu2 | 15680bg1 | \([0, -1, 0, 7775, 15905]\) | \(34391/20\) | \(-30224159866880\) | \([]\) | \(32256\) | \(1.2761\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15680.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 15680.bu do not have complex multiplication.Modular form 15680.2.a.bu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.