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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 28566.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28566.bl1 | 28566bc3 | \([1, -1, 1, -15176, 732673]\) | \(-132651/2\) | \(-5827580806374\) | \([]\) | \(71280\) | \(1.2525\) | |
28566.bl2 | 28566bc2 | \([1, -1, 1, -7241, -312631]\) | \(-1167051/512\) | \(-18418033165824\) | \([]\) | \(71280\) | \(1.2525\) | |
28566.bl3 | 28566bc1 | \([1, -1, 1, 694, 4769]\) | \(9261/8\) | \(-31975752024\) | \([]\) | \(23760\) | \(0.70324\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28566.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 28566.bl do not have complex multiplication.Modular form 28566.2.a.bl
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.