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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 67270bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 67270.y2 | 67270bp1 | \([1, 0, 0, 14395, 2714077]\) | \(371694959/3797500\) | \(-3370295228597500\) | \([2]\) | \(491520\) | \(1.6606\) | \(\Gamma_0(N)\)-optimal |
| 67270.y1 | 67270bp2 | \([1, 0, 0, -225855, 38319127]\) | \(1435630901041/115368050\) | \(102389569044792050\) | \([2]\) | \(983040\) | \(2.0071\) |
Rank
sage: E.rank()
The elliptic curves in class 67270bp have rank \(1\).
Complex multiplication
The elliptic curves in class 67270bp do not have complex multiplication.Modular form 67270.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
