Cremona's table of elliptic curves

2028 = 2² · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 13+	Signs for the Atkin-Lehner involutions
Class	2028d	Isogeny class
Conductor	2028	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	1527047909712 = 24 · 32 · 139	Discriminant
Eigenvalues	2- 3-  0 -2  0 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-123933,-16834284]	[a1,a2,a3,a4,a6]
Generators	[1200:39546:1]	Generators of the group modulo torsion
j	2725888000000/19773	j-invariant
L	3.3722029580321	L(r)(E,1)/r!
Ω	0.25445014987574	Real period
R	2.208817037888	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	8112t3 32448b3 6084f3 50700d3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2028d3

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

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Quadratic twists for elliptic curve 2028d3

-4	8	-3	5	-7	13
8112t3	32448b3	6084f3	50700d3	99372f3	156b3

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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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