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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 97461.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97461.q1 | 97461m6 | \([1, -1, 0, -8896743, -10210176684]\) | \(908031902324522977/161726530797\) | \(13870657209245728437\) | \([2]\) | \(3145728\) | \(2.6774\) | |
| 97461.q2 | 97461m4 | \([1, -1, 0, -612558, -125009865]\) | \(296380748763217/92608836489\) | \(7942700675984789169\) | \([2, 2]\) | \(1572864\) | \(2.3308\) | |
| 97461.q3 | 97461m2 | \([1, -1, 0, -239913, 43798320]\) | \(17806161424897/668584449\) | \(57341894751652329\) | \([2, 2]\) | \(786432\) | \(1.9843\) | |
| 97461.q4 | 97461m1 | \([1, -1, 0, -237708, 44667531]\) | \(17319700013617/25857\) | \(2217654590697\) | \([2]\) | \(393216\) | \(1.6377\) | \(\Gamma_0(N)\)-optimal |
| 97461.q5 | 97461m3 | \([1, -1, 0, 97452, 156950541]\) | \(1193377118543/124806800313\) | \(-10704195137267595873\) | \([2]\) | \(1572864\) | \(2.3308\) | |
| 97461.q6 | 97461m5 | \([1, -1, 0, 1709307, -848038626]\) | \(6439735268725823/7345472585373\) | \(-629992690559283548133\) | \([2]\) | \(3145728\) | \(2.6774\) |
Rank
sage: E.rank()
The elliptic curves in class 97461.q have rank \(0\).
Complex multiplication
The elliptic curves in class 97461.q do not have complex multiplication.Modular form 97461.2.a.q
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.
