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
deg	2016	Modular degree for the optimal curve
Δ	731898702288 = 24 · 36 · 137	Discriminant
Eigenvalues	2- 3-  0 -2  0 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2253,144]	[a1,a2,a3,a4,a6]
Generators	[108:1014:1]	Generators of the group modulo torsion
j	16384000/9477	j-invariant
L	3.3722029580321	L(r)(E,1)/r!
Ω	0.76335044962721	Real period
R	0.73627234596267	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	8112t1 32448b1 6084f1 50700d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2028d1

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 2028d1

-4	8	-3	5	-7	13
8112t1	32448b1	6084f1	50700d1	99372f1	156b1

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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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