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	22800bk	Isogeny class
Conductor	22800	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	9600	Modular degree for the optimal curve
Δ	356250000 = 24 · 3 · 58 · 19	Discriminant
Eigenvalues	2+ 3- 5-  3 -6 -2  0 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-708,6963]	[a1,a2,a3,a4,a6]
Generators	[-31:9:1]	Generators of the group modulo torsion
j	6288640/57	j-invariant
L	6.548058123189	L(r)(E,1)/r!
Ω	1.7100992079911	Real period
R	3.8290516085797	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	11400i1 91200he1 68400cp1 22800e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22800bk1

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
+	-	-	3	-6	-2	0	+	2	-3	0	-2	7	4	4	-3	3	7	-16	9	-9	-2	-4	-1	8

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Quadratic twists for elliptic curve 22800bk1

-4	8	-3	5
11400i1	91200he1	68400cp1	22800e1

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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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