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	22800cz	Isogeny class
Conductor	22800	Conductor
∏ cp	160	Product of Tamagawa factors cp
deg	61440	Modular degree for the optimal curve
Δ	-28071360000000 = -1 · 212 · 35 · 57 · 192	Discriminant
Eigenvalues	2- 3- 5+ -2  6  0  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,7592,15188]	[a1,a2,a3,a4,a6]
Generators	[38:600:1]	Generators of the group modulo torsion
j	756058031/438615	j-invariant
L	6.7098010452191	L(r)(E,1)/r!
Ω	0.39979305366779	Real period
R	0.41957964149588	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	1425c1 91200gd1 68400ep1 4560k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22800cz1

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	6	0	6	+	-8	4	0	-4	0	-2	-8	-2	-12	2	-8	-16	-14	-8	0	0	12

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Quadratic twists for elliptic curve 22800cz1

-4	8	-3	5
1425c1	91200gd1	68400ep1	4560k1

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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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