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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 39600.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39600.bl1 | 39600dy3 | \([0, 0, 0, -28153200, -57496282000]\) | \(-52893159101157376/11\) | \(-513216000000\) | \([]\) | \(840000\) | \(2.5439\) | |
39600.bl2 | 39600dy2 | \([0, 0, 0, -37200, -5002000]\) | \(-122023936/161051\) | \(-7513995456000000\) | \([]\) | \(168000\) | \(1.7392\) | |
39600.bl3 | 39600dy1 | \([0, 0, 0, -1200, 38000]\) | \(-4096/11\) | \(-513216000000\) | \([]\) | \(33600\) | \(0.93444\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39600.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 39600.bl do not have complex multiplication.Modular form 39600.2.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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.