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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 11550.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11550.f1 | 11550n4 | \([1, 1, 0, -166369450, 825866396500]\) | \(260744057755293612689909/8504954620259328\) | \(16611239492694000000000\) | \([2]\) | \(1920000\) | \(3.3577\) | |
| 11550.f2 | 11550n3 | \([1, 1, 0, -10849450, 11719196500]\) | \(72313087342699809269/11447096545640448\) | \(22357610440704000000000\) | \([2]\) | \(960000\) | \(3.0111\) | |
| 11550.f3 | 11550n2 | \([1, 1, 0, -2943825, -1927500375]\) | \(1444540994277943589/15251205665388\) | \(29787511065210937500\) | \([2]\) | \(384000\) | \(2.5530\) | |
| 11550.f4 | 11550n1 | \([1, 1, 0, -2936325, -1937887875]\) | \(1433528304665250149/162339408\) | \(317069156250000\) | \([2]\) | \(192000\) | \(2.2064\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11550.f have rank \(1\).
Complex multiplication
The elliptic curves in class 11550.f do not have complex multiplication.Modular form 11550.2.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 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.
