Show commands:
SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 235950.dd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235950.dd1 | 235950dd3 | \([1, 0, 1, -1462651, 680618948]\) | \(12501706118329/2570490\) | \(71152809920156250\) | \([2]\) | \(4423680\) | \(2.2307\) | |
| 235950.dd2 | 235950dd2 | \([1, 0, 1, -101401, 8161448]\) | \(4165509529/1368900\) | \(37892028951562500\) | \([2, 2]\) | \(2211840\) | \(1.8841\) | |
| 235950.dd3 | 235950dd1 | \([1, 0, 1, -40901, -3091552]\) | \(273359449/9360\) | \(259090796250000\) | \([2]\) | \(1105920\) | \(1.5376\) | \(\Gamma_0(N)\)-optimal |
| 235950.dd4 | 235950dd4 | \([1, 0, 1, 291849, 56137948]\) | \(99317171591/106616250\) | \(-2951206101035156250\) | \([2]\) | \(4423680\) | \(2.2307\) |
Rank
sage: E.rank()
The elliptic curves in class 235950.dd have rank \(1\).
Complex multiplication
The elliptic curves in class 235950.dd do not have complex multiplication.Modular form 235950.2.a.dd
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
