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	22800cm	Isogeny class
Conductor	22800	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	46080	Modular degree for the optimal curve
Δ	-3025797120000 = -1 · 220 · 35 · 54 · 19	Discriminant
Eigenvalues	2- 3+ 5-  4  1  0 -8 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8208,-295488]	[a1,a2,a3,a4,a6]
Generators	[122:710:1]	Generators of the group modulo torsion
j	-23891790625/1181952	j-invariant
L	5.0946161867752	L(r)(E,1)/r!
Ω	0.25006636474965	Real period
R	3.3955094226524	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	2850bb1 91200jj1 68400gb1 22800dc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22800cm1

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
-	+	-	4	1	0	-8	+	3	-1	-1	-2	-10	8	0	3	-4	5	5	6	-13	5	-11	3	10

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Quadratic twists for elliptic curve 22800cm1

-4	8	-3	5
2850bb1	91200jj1	68400gb1	22800dc1

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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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