Show commands for:
SageMath
sage: E = EllipticCurve("s1")
sage: E.isogeny_class()
Elliptic curves in class 97461.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 97461.s1 | 97461l6 | [1, -1, 0, -17895348, -29112590781] | [2] | 4718592 | |
| 97461.s2 | 97461l4 | [1, -1, 0, -1364463, -239747040] | [2, 2] | 2359296 | |
| 97461.s3 | 97461l2 | [1, -1, 0, -727218, 236274975] | [2, 2] | 1179648 | |
| 97461.s4 | 97461l1 | [1, -1, 0, -725013, 237792456] | [2] | 589824 | \(\Gamma_0(N)\)-optimal |
| 97461.s5 | 97461l3 | [1, -1, 0, -125253, 615151746] | [2] | 2359296 | |
| 97461.s6 | 97461l5 | [1, -1, 0, 4970502, -1839959199] | [2] | 4718592 |
Rank
sage: E.rank()
The elliptic curves in class 97461.s have rank \(0\).
Complex multiplication
The elliptic curves in class 97461.s do not have complex multiplication.Modular form 97461.2.a.s
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
