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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 476850f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 476850.f4 | 476850f1 | \([1, 1, 0, -14600, 6000]\) | \(912673/528\) | \(199134944250000\) | \([2]\) | \(2621440\) | \(1.4332\) | \(\Gamma_0(N)\)-optimal |
| 476850.f2 | 476850f2 | \([1, 1, 0, -159100, -24414500]\) | \(1180932193/4356\) | \(1642863290062500\) | \([2, 2]\) | \(5242880\) | \(1.7798\) | |
| 476850.f3 | 476850f3 | \([1, 1, 0, -86850, -46595250]\) | \(-192100033/2371842\) | \(-894539061439031250\) | \([2]\) | \(10485760\) | \(2.1264\) | |
| 476850.f1 | 476850f4 | \([1, 1, 0, -2543350, -1562255750]\) | \(4824238966273/66\) | \(24891868031250\) | \([2]\) | \(10485760\) | \(2.1264\) |
Rank
sage: E.rank()
The elliptic curves in class 476850f have rank \(0\).
Complex multiplication
The elliptic curves in class 476850f do not have complex multiplication.Modular form 476850.2.a.f
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.
