Cremona's table of elliptic curves

45600 = 2⁵ · 3 · 5² · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 19-	Signs for the Atkin-Lehner involutions
Class	45600bw	Isogeny class
Conductor	45600	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1368000000 = 29 · 32 · 56 · 19	Discriminant
Eigenvalues	2- 3- 5+ -4 -4 -2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-45608,3733788]	[a1,a2,a3,a4,a6]
Generators	[127:78:1] [159:726:1]	Generators of the group modulo torsion
j	1311494070536/171	j-invariant
L	9.8084791495933	L(r)(E,1)/r!
Ω	1.1834254489127	Real period
R	8.2882104306656	Regulator
r	2	Rank of the group of rational points
S	0.99999999999995	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	45600c4 91200n4 1824c3	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 45600bw4

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	-2	-2	-	-4	-6	0	-2	-6	-12	-4	-2	12	-10	-4	0	-10	8	-12	-14	-10

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Quadratic twists for elliptic curve 45600bw4

-4	8	5
45600c4	91200n4	1824c3

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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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