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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 3600bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3600.bk1 | 3600bp1 | \([0, 0, 0, -1200, -16400]\) | \(-102400/3\) | \(-5598720000\) | \([]\) | \(1920\) | \(0.64935\) | \(\Gamma_0(N)\)-optimal |
3600.bk2 | 3600bp2 | \([0, 0, 0, 6000, 790000]\) | \(20480/243\) | \(-283435200000000\) | \([]\) | \(9600\) | \(1.4541\) |
Rank
sage: E.rank()
The elliptic curves in class 3600bp have rank \(0\).
Complex multiplication
The elliptic curves in class 3600bp do not have complex multiplication.Modular form 3600.2.a.bp
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.