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	45600bn	Isogeny class
Conductor	45600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	57000000 = 26 · 3 · 56 · 19	Discriminant
Eigenvalues	2- 3- 5+  0  0  0  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-458,-3912]	[a1,a2,a3,a4,a6]
Generators	[4719:62074:27]	Generators of the group modulo torsion
j	10648000/57	j-invariant
L	7.6697205688575	L(r)(E,1)/r!
Ω	1.0321531888886	Real period
R	7.4307967571261	Regulator
r	1	Rank of the group of rational points
S	1.0000000000008	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	45600e1 91200r1 1824a1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 45600bn1

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

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Quadratic twists for elliptic curve 45600bn1

-4	8	5
45600e1	91200r1	1824a1

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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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