Cremona's table of elliptic curves

22050 = 2 · 3² · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	22050ek	Isogeny class
Conductor	22050	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	80640	Modular degree for the optimal curve
Δ	-247109347825200 = -1 · 24 · 37 · 52 · 710	Discriminant
Eigenvalues	2- 3- 5+ 7-  4  1 -2 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-11255,887807]	[a1,a2,a3,a4,a6]
j	-30625/48	j-invariant
L	3.9830122611691	L(r)(E,1)/r!
Ω	0.49787653264614	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7350ba1 22050cs1 22050dv1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 22050ek1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	+	-	4	1	-2	-1	-2	-4	0	-3	12	-8	6	2	6	13	-3	-16	-11	13	6	-2	17

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Quadratic twists for elliptic curve 22050ek1

-3	5	-7
7350ba1	22050cs1	22050dv1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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