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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 7200.bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7200.bp1 | 7200j1 | \([0, 0, 0, -1425, -20500]\) | \(438976/5\) | \(3645000000\) | \([2]\) | \(4608\) | \(0.64798\) | \(\Gamma_0(N)\)-optimal |
7200.bp2 | 7200j2 | \([0, 0, 0, -300, -52000]\) | \(-64/25\) | \(-1166400000000\) | \([2]\) | \(9216\) | \(0.99455\) |
Rank
sage: E.rank()
The elliptic curves in class 7200.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 7200.bp do not have complex multiplication.Modular form 7200.2.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 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.