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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 120240.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 120240.bp1 | 120240bv2 | \([0, 0, 0, -9027, 321346]\) | \(735580702683/22311200\) | \(2467440230400\) | \([2]\) | \(153600\) | \(1.1540\) | |
| 120240.bp2 | 120240bv1 | \([0, 0, 0, -1347, -11966]\) | \(2444008923/855040\) | \(94560583680\) | \([2]\) | \(76800\) | \(0.80747\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 120240.bp have rank \(2\).
Complex multiplication
The elliptic curves in class 120240.bp do not have complex multiplication.Modular form 120240.2.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.
