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	2028b	Isogeny class
Conductor	2028	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	504	Modular degree for the optimal curve
Δ	-94618368 = -1 · 28 · 37 · 132	Discriminant
Eigenvalues	2- 3+ -2 -1 -2 13+ -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-69,-495]	[a1,a2,a3,a4,a6]
j	-851968/2187	j-invariant
L	0.7697057749909	L(r)(E,1)/r!
Ω	0.7697057749909	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8112bf1 32448bc1 6084g1 50700w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2028b1

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
-	+	-2	-1	-2	+	-4	-4	6	6	1	-10	4	1	10	8	2	-5	7	-10	7	17	-12	16	-13

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Quadratic twists for elliptic curve 2028b1

-4	8	-3	5	-7	13
8112bf1	32448bc1	6084g1	50700w1	99372bl1	2028a1

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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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