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	22800bc	Isogeny class
Conductor	22800	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	4222400400000000 = 210 · 34 · 58 · 194	Discriminant
Eigenvalues	2+ 3- 5+  0 -4  2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1083008,433433988]	[a1,a2,a3,a4,a6]
Generators	[223:14250:1]	Generators of the group modulo torsion
j	8780093172522724/263900025	j-invariant
L	6.2097716726347	L(r)(E,1)/r!
Ω	0.40795703196335	Real period
R	0.95135197859399	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	11400a3 91200fa4 68400bv4 4560d4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22800bc4

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	-	0	6	0	-6	-6	4	8	-6	12	-2	4	-8	6	-16	-4	-6	-10

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Quadratic twists for elliptic curve 22800bc4

-4	8	-3	5
11400a3	91200fa4	68400bv4	4560d4

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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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