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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 816.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 816.d1 | 816e3 | \([0, -1, 0, -12008, 386928]\) | \(46753267515625/11591221248\) | \(47477642231808\) | \([2]\) | \(1728\) | \(1.3346\) | |
| 816.d2 | 816e1 | \([0, -1, 0, -4088, -99216]\) | \(1845026709625/793152\) | \(3248750592\) | \([2]\) | \(576\) | \(0.78527\) | \(\Gamma_0(N)\)-optimal |
| 816.d3 | 816e2 | \([0, -1, 0, -3448, -131984]\) | \(-1107111813625/1228691592\) | \(-5032720760832\) | \([2]\) | \(1152\) | \(1.1318\) | |
| 816.d4 | 816e4 | \([0, -1, 0, 28952, 2418544]\) | \(655215969476375/1001033261568\) | \(-4100232239382528\) | \([2]\) | \(3456\) | \(1.6811\) |
Rank
sage: E.rank()
The elliptic curves in class 816.d have rank \(0\).
Complex multiplication
The elliptic curves in class 816.d do not have complex multiplication.Modular form 816.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
