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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 39039.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39039.v1 | 39039w1 | \([1, 0, 1, -509839711, -4430955601291]\) | \(1382084250541230782125/19771083137421\) | \(209662438734311867337033\) | \([2]\) | \(9831744\) | \(3.6143\) | \(\Gamma_0(N)\)-optimal |
39039.v2 | 39039w2 | \([1, 0, 1, -495218676, -4697035044635]\) | \(-1266556547153680328125/165777947457789051\) | \(-1757992139873350935295765023\) | \([2]\) | \(19663488\) | \(3.9609\) |
Rank
sage: E.rank()
The elliptic curves in class 39039.v have rank \(0\).
Complex multiplication
The elliptic curves in class 39039.v do not have complex multiplication.Modular form 39039.2.a.v
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.