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SageMath
E = EllipticCurve("dw1")
E.isogeny_class()
Elliptic curves in class 48510.dw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48510.dw1 | 48510ef4 | \([1, -1, 1, -117355622, 489361726221]\) | \(2084105208962185000201/31185000\) | \(2674616483385000\) | \([2]\) | \(4718592\) | \(2.9638\) | |
| 48510.dw2 | 48510ef3 | \([1, -1, 1, -7952342, 6284455629]\) | \(648474704552553481/176469171805080\) | \(15135076341804279694680\) | \([2]\) | \(4718592\) | \(2.9638\) | |
| 48510.dw3 | 48510ef2 | \([1, -1, 1, -7334942, 7647180909]\) | \(508859562767519881/62240270400\) | \(5338106562199118400\) | \([2, 2]\) | \(2359296\) | \(2.6172\) | |
| 48510.dw4 | 48510ef1 | \([1, -1, 1, -420062, 140387181]\) | \(-95575628340361/43812679680\) | \(-3757643586769121280\) | \([2]\) | \(1179648\) | \(2.2706\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 48510.dw have rank \(0\).
Complex multiplication
The elliptic curves in class 48510.dw do not have complex multiplication.Modular form 48510.2.a.dw
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.
