Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 95506a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95506.e4 | 95506a1 | \([1, 1, 0, -8485, 182733]\) | \(3048625/1088\) | \(24114824908352\) | \([2]\) | \(299520\) | \(1.2688\) | \(\Gamma_0(N)\)-optimal |
95506.e3 | 95506a2 | \([1, 1, 0, -120845, 16115381]\) | \(8805624625/2312\) | \(51244002930248\) | \([2]\) | \(599040\) | \(1.6153\) | |
95506.e2 | 95506a3 | \([1, 1, 0, -289385, -60030991]\) | \(120920208625/19652\) | \(435574024907108\) | \([2]\) | \(898560\) | \(1.8181\) | |
95506.e1 | 95506a4 | \([1, 1, 0, -317475, -47710717]\) | \(159661140625/48275138\) | \(1069987592184310802\) | \([2]\) | \(1797120\) | \(2.1646\) |
Rank
sage: E.rank()
The elliptic curves in class 95506a have rank \(1\).
Complex multiplication
The elliptic curves in class 95506a do not have complex multiplication.Modular form 95506.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.