Show commands:
SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 190575be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190575.bp3 | 190575be1 | \([1, -1, 1, -68630, 6573372]\) | \(1771561/105\) | \(2118814636640625\) | \([2]\) | \(1105920\) | \(1.6939\) | \(\Gamma_0(N)\)-optimal |
| 190575.bp2 | 190575be2 | \([1, -1, 1, -204755, -27457878]\) | \(47045881/11025\) | \(222475536847265625\) | \([2, 2]\) | \(2211840\) | \(2.0404\) | |
| 190575.bp4 | 190575be3 | \([1, -1, 1, 475870, -171750378]\) | \(590589719/972405\) | \(-19622342349928828125\) | \([2]\) | \(4423680\) | \(2.3870\) | |
| 190575.bp1 | 190575be4 | \([1, -1, 1, -3063380, -2062798878]\) | \(157551496201/13125\) | \(264851829580078125\) | \([2]\) | \(4423680\) | \(2.3870\) |
Rank
sage: E.rank()
The elliptic curves in class 190575be have rank \(0\).
Complex multiplication
The elliptic curves in class 190575be do not have complex multiplication.Modular form 190575.2.a.be
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
