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	22050dw	Isogeny class
Conductor	22050	Conductor
∏ cp	104	Product of Tamagawa factors cp
deg	599040	Modular degree for the optimal curve
Δ	-6301184400000000000 = -1 · 213 · 38 · 511 · 74	Discriminant
Eigenvalues	2- 3- 5+ 7+  5  5 -4 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-672755,-244158253]	[a1,a2,a3,a4,a6]
Generators	[2139:88930:1]	Generators of the group modulo torsion
j	-1231272543361/230400000	j-invariant
L	8.7581530197303	L(r)(E,1)/r!
Ω	0.082512883577355	Real period
R	1.0206043729662	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7350v1 4410g1 22050et1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 22050dw1

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
-	-	+	+	5	5	-4	-7	1	0	-2	-1	-5	-12	-11	-9	-4	4	12	-2	-10	-12	-12	-14	8

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Quadratic twists for elliptic curve 22050dw1

-3	5	-7
7350v1	4410g1	22050et1

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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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