Cremona's table of elliptic curves

22800 = 2⁴ · 3 · 5² · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 19+	Signs for the Atkin-Lehner involutions
Class	22800br	Isogeny class
Conductor	22800	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	3465600000000 = 213 · 3 · 58 · 192	Discriminant
Eigenvalues	2- 3+ 5+ -2  0 -6 -8 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-12008,502512]	[a1,a2,a3,a4,a6]
Generators	[-68:1000:1] [-38:950:1]	Generators of the group modulo torsion
j	2992209121/54150	j-invariant
L	6.3080342665292	L(r)(E,1)/r!
Ω	0.79249628237147	Real period
R	0.99496275358737	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2850k2 91200ie2 68400ek2 4560ba2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22800br2

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
-	+	+	-2	0	-6	-8	+	-4	2	2	2	-12	4	12	-10	-6	-14	-12	8	10	-14	2	0	-2

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Quadratic twists for elliptic curve 22800br2

-4	8	-3	5
2850k2	91200ie2	68400ek2	4560ba2

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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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