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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 297024q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 297024.q3 | 297024q1 | \([0, -1, 0, -8416884, 9400979574]\) | \(1030380937103248652484928/86968281646970451\) | \(5565970025406108864\) | \([2]\) | \(8601600\) | \(2.6401\) | \(\Gamma_0(N)\)-optimal |
| 297024.q2 | 297024q2 | \([0, -1, 0, -9005129, 8012133129]\) | \(19716672739677796891072/4644693474883838649\) | \(19024664473124203106304\) | \([2, 2]\) | \(17203200\) | \(2.9867\) | |
| 297024.q4 | 297024q3 | \([0, -1, 0, 21000511, 50038032513]\) | \(31258155245948891455096/51107590582503108381\) | \(-1674693528207461855428608\) | \([2]\) | \(34406400\) | \(3.3332\) | |
| 297024.q1 | 297024q4 | \([0, -1, 0, -48422689, -122909350655]\) | \(383195583457547406751304/22543683480024312879\) | \(738711420273436684419072\) | \([2]\) | \(34406400\) | \(3.3332\) |
Rank
sage: E.rank()
The elliptic curves in class 297024q have rank \(1\).
Complex multiplication
The elliptic curves in class 297024q do not have complex multiplication.Modular form 297024.2.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 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.
