Cremona's table of elliptic curves

4512 = 2⁵ · 3 · 47

Field	Data	Notes
Atkin-Lehner	2- 3- 47+	Signs for the Atkin-Lehner involutions
Class	4512p	Isogeny class
Conductor	4512	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	10179072 = 29 · 32 · 472	Discriminant
Eigenvalues	2- 3- -4  0 -2 -4  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-80,204]	[a1,a2,a3,a4,a6]
Generators	[7:6:1]	Generators of the group modulo torsion
j	111980168/19881	j-invariant
L	3.4114525606323	L(r)(E,1)/r!
Ω	2.1800234518967	Real period
R	1.5648696612251	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4512k2 9024bg2 13536q2 112800h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4512p2

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	0	-2	-4	6	6	4	0	-8	2	10	-10	+	-6	8	2	-14	16	-14	-8	-12	-10	2

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Quadratic twists for elliptic curve 4512p2

-4	8	-3	5
4512k2	9024bg2	13536q2	112800h2

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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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