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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 11550.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11550.l1 | 11550g3 | \([1, 1, 0, -2420775, 1448695125]\) | \(100407751863770656369/166028940000\) | \(2594202187500000\) | \([2]\) | \(245760\) | \(2.2204\) | |
| 11550.l2 | 11550g2 | \([1, 1, 0, -152775, 22123125]\) | \(25238585142450289/995844326400\) | \(15560067600000000\) | \([2, 2]\) | \(122880\) | \(1.8738\) | |
| 11550.l3 | 11550g1 | \([1, 1, 0, -24775, -1044875]\) | \(107639597521009/32699842560\) | \(510935040000000\) | \([2]\) | \(61440\) | \(1.5273\) | \(\Gamma_0(N)\)-optimal |
| 11550.l4 | 11550g4 | \([1, 1, 0, 67225, 80863125]\) | \(2150235484224911/181905111732960\) | \(-2842267370827500000\) | \([2]\) | \(245760\) | \(2.2204\) |
Rank
sage: E.rank()
The elliptic curves in class 11550.l have rank \(0\).
Complex multiplication
The elliptic curves in class 11550.l do not have complex multiplication.Modular form 11550.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
