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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 350064.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350064.n1 | 350064n4 | \([0, 0, 0, -18651835731, -980461368264350]\) | \(961304494694784944316951544132/20823839690665869\) | \(15544913033723308545024\) | \([2]\) | \(237109248\) | \(4.2368\) | |
| 350064.n2 | 350064n2 | \([0, 0, 0, -1165780911, -15318572474450]\) | \(938873405985183095624413648/138168614163375007641\) | \(25785579449625697425993984\) | \([2, 2]\) | \(118554624\) | \(3.8902\) | |
| 350064.n3 | 350064n3 | \([0, 0, 0, -1058775771, -18244456819526]\) | \(-175836167856967771687798372/90870391656586224332793\) | \(-67834383890074990119532643328\) | \([2]\) | \(237109248\) | \(4.2368\) | |
| 350064.n4 | 350064n1 | \([0, 0, 0, -79590306, -192499347341]\) | \(4780317300004724587829248/1393942929106031774613\) | \(16258950325092754619086032\) | \([2]\) | \(59277312\) | \(3.5436\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 350064.n have rank \(0\).
Complex multiplication
The elliptic curves in class 350064.n do not have complex multiplication.Modular form 350064.2.a.n
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.
