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	45600c	Isogeny class
Conductor	45600	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	7978176000000 = 212 · 38 · 56 · 19	Discriminant
Eigenvalues	2+ 3+ 5+  4  4 -2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5233,54337]	[a1,a2,a3,a4,a6]
Generators	[87:500:1]	Generators of the group modulo torsion
j	247673152/124659	j-invariant
L	6.2881786423027	L(r)(E,1)/r!
Ω	0.65338401189263	Real period
R	2.4060041751295	Regulator
r	1	Rank of the group of rational points
S	0.99999999999945	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	45600bw3 91200dz1 1824i3	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 45600c3

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 45600c3

-4	8	5
45600bw3	91200dz1	1824i3

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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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