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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 7920.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7920.n1 | 7920u3 | \([0, 0, 0, -1545723, 739681578]\) | \(5066026756449723/11000000\) | \(886837248000000\) | \([2]\) | \(124416\) | \(2.1151\) | |
| 7920.n2 | 7920u4 | \([0, 0, 0, -1528443, 757027242]\) | \(-4898016158612283/236328125000\) | \(-19053144000000000000\) | \([2]\) | \(248832\) | \(2.4616\) | |
| 7920.n3 | 7920u1 | \([0, 0, 0, -25083, 323882]\) | \(15781142246787/8722841600\) | \(964676498227200\) | \([2]\) | \(41472\) | \(1.5657\) | \(\Gamma_0(N)\)-optimal |
| 7920.n4 | 7920u2 | \([0, 0, 0, 97797, 2560298]\) | \(935355271080573/566899520000\) | \(-62694551715840000\) | \([2]\) | \(82944\) | \(1.9123\) |
Rank
sage: E.rank()
The elliptic curves in class 7920.n have rank \(0\).
Complex multiplication
The elliptic curves in class 7920.n do not have complex multiplication.Modular form 7920.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
