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	22800bp	Isogeny class
Conductor	22800	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	16896	Modular degree for the optimal curve
Δ	-1772928000 = -1 · 210 · 36 · 53 · 19	Discriminant
Eigenvalues	2+ 3- 5- -4 -4 -6 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-328,2948]	[a1,a2,a3,a4,a6]
Generators	[-16:66:1] [2:48:1]	Generators of the group modulo torsion
j	-30581492/13851	j-invariant
L	8.0226255384435	L(r)(E,1)/r!
Ω	1.3918065414973	Real period
R	0.48034845955274	Regulator
r	2	Rank of the group of rational points
S	0.99999999999994	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11400be1 91200ha1 68400dc1 22800t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22800bp1

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	-4	-6	-2	-	-6	-10	2	6	-12	-2	-6	-6	-14	-6	8	-4	-8	10	16	-16	14

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Quadratic twists for elliptic curve 22800bp1

-4	8	-3	5
11400be1	91200ha1	68400dc1	22800t1

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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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