Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 127050.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 127050.q1 | 127050d4 | \([1, 1, 0, -804990375, -8791251721875]\) | \(2084105208962185000201/31185000\) | \(863220777890625000\) | \([2]\) | \(35389440\) | \(3.4452\) | |
| 127050.q2 | 127050d3 | \([1, 1, 0, -54548375, -112888027875]\) | \(648474704552553481/176469171805080\) | \(4884779726127802029375000\) | \([2]\) | \(35389440\) | \(3.4452\) | |
| 127050.q3 | 127050d2 | \([1, 1, 0, -50313375, -137370562875]\) | \(508859562767519881/62240270400\) | \(1722850557345225000000\) | \([2, 2]\) | \(17694720\) | \(3.0986\) | |
| 127050.q4 | 127050d1 | \([1, 1, 0, -2881375, -2521386875]\) | \(-95575628340361/43812679680\) | \(-1212763041040320000000\) | \([2]\) | \(8847360\) | \(2.7520\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 127050.q have rank \(0\).
Complex multiplication
The elliptic curves in class 127050.q do not have complex multiplication.Modular form 127050.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
