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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 83259.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83259.n1 | 83259c2 | \([1, -1, 0, -1318425, 582796088]\) | \(21647657403/9251\) | \(108309851609424993\) | \([2]\) | \(2338560\) | \(2.2291\) | |
83259.n2 | 83259c1 | \([1, -1, 0, -69540, 12055643]\) | \(-3176523/3509\) | \(-41083047162195687\) | \([2]\) | \(1169280\) | \(1.8825\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 83259.n have rank \(0\).
Complex multiplication
The elliptic curves in class 83259.n do not have complex multiplication.Modular form 83259.2.a.n
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.