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	22800ca	Isogeny class
Conductor	22800	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2850000000000000 = 213 · 3 · 514 · 19	Discriminant
Eigenvalues	2- 3+ 5+  0 -4 -2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-248408,47667312]	[a1,a2,a3,a4,a6]
Generators	[306:462:1]	Generators of the group modulo torsion
j	26487576322129/44531250	j-invariant
L	3.8642272151746	L(r)(E,1)/r!
Ω	0.45253476442533	Real period
R	4.2695363085328	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2850i3 91200hk4 68400fa4 4560x3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22800ca4

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

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Quadratic twists for elliptic curve 22800ca4

-4	8	-3	5
2850i3	91200hk4	68400fa4	4560x3

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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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