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SageMath
E = EllipticCurve("gn1")
E.isogeny_class()
Elliptic curves in class 129360gn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129360.ey4 | 129360gn1 | \([0, 1, 0, -746776, 332271764]\) | \(-95575628340361/43812679680\) | \(-21112905530049822720\) | \([2]\) | \(3538944\) | \(2.4145\) | \(\Gamma_0(N)\)-optimal |
| 129360.ey3 | 129360gn2 | \([0, 1, 0, -13039896, 18117957780]\) | \(508859562767519881/62240270400\) | \(29992982824098201600\) | \([2, 2]\) | \(7077888\) | \(2.7611\) | |
| 129360.ey2 | 129360gn3 | \([0, 1, 0, -14137496, 14887062420]\) | \(648474704552553481/176469171805080\) | \(85038782847778229944320\) | \([2]\) | \(14155776\) | \(3.1076\) | |
| 129360.ey1 | 129360gn4 | \([0, 1, 0, -208632216, 1159829448084]\) | \(2084105208962185000201/31185000\) | \(15027749130240000\) | \([2]\) | \(14155776\) | \(3.1076\) |
Rank
sage: E.rank()
The elliptic curves in class 129360gn have rank \(1\).
Complex multiplication
The elliptic curves in class 129360gn do not have complex multiplication.Modular form 129360.2.a.gn
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 Cremona 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 Cremona labels.
