Show commands:
SageMath
E = EllipticCurve("ia1")
E.isogeny_class()
Elliptic curves in class 91200.ia
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91200.ia1 | 91200dv4 | \([0, 1, 0, -84517512033, -9457350036263937]\) | \(16300610738133468173382620881/2228489100\) | \(9127891353600000000\) | \([2]\) | \(110592000\) | \(4.4533\) | |
| 91200.ia2 | 91200dv3 | \([0, 1, 0, -5282344033, -147772442439937]\) | \(-3979640234041473454886161/1471455901872240\) | \(-6027083374068695040000000\) | \([2]\) | \(55296000\) | \(4.1067\) | |
| 91200.ia3 | 91200dv2 | \([0, 1, 0, -140712033, -553560263937]\) | \(75224183150104868881/11219310000000000\) | \(45954293760000000000000000\) | \([2]\) | \(22118400\) | \(3.6485\) | |
| 91200.ia4 | 91200dv1 | \([0, 1, 0, 14935967, -47237319937]\) | \(89962967236397039/287450726400000\) | \(-1177398175334400000000000\) | \([2]\) | \(11059200\) | \(3.3020\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91200.ia have rank \(1\).
Complex multiplication
The elliptic curves in class 91200.ia do not have complex multiplication.Modular form 91200.2.a.ia
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
