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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 202160.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202160.bp1 | 202160cm1 | \([0, 0, 0, -397822, -96567861]\) | \(1348614144/175\) | \(903525553781200\) | \([2]\) | \(1556480\) | \(1.8905\) | \(\Gamma_0(N)\)-optimal |
| 202160.bp2 | 202160cm2 | \([0, 0, 0, -363527, -113900554]\) | \(-64314864/30625\) | \(-2529871550587360000\) | \([2]\) | \(3112960\) | \(2.2370\) |
Rank
sage: E.rank()
The elliptic curves in class 202160.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 202160.bp do not have complex multiplication.Modular form 202160.2.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.
