Show commands:
SageMath
E = EllipticCurve("fg1")
E.isogeny_class()
Elliptic curves in class 91200fg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91200.bn4 | 91200fg1 | \([0, -1, 0, 14935967, 47237319937]\) | \(89962967236397039/287450726400000\) | \(-1177398175334400000000000\) | \([2]\) | \(11059200\) | \(3.3020\) | \(\Gamma_0(N)\)-optimal |
| 91200.bn3 | 91200fg2 | \([0, -1, 0, -140712033, 553560263937]\) | \(75224183150104868881/11219310000000000\) | \(45954293760000000000000000\) | \([2]\) | \(22118400\) | \(3.6485\) | |
| 91200.bn2 | 91200fg3 | \([0, -1, 0, -5282344033, 147772442439937]\) | \(-3979640234041473454886161/1471455901872240\) | \(-6027083374068695040000000\) | \([2]\) | \(55296000\) | \(4.1067\) | |
| 91200.bn1 | 91200fg4 | \([0, -1, 0, -84517512033, 9457350036263937]\) | \(16300610738133468173382620881/2228489100\) | \(9127891353600000000\) | \([2]\) | \(110592000\) | \(4.4533\) |
Rank
sage: E.rank()
The elliptic curves in class 91200fg have rank \(0\).
Complex multiplication
The elliptic curves in class 91200fg do not have complex multiplication.Modular form 91200.2.a.fg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
