Cremona's table of elliptic curves

4028 = 2² · 19 · 53

Field	Data	Notes
Atkin-Lehner	2- 19- 53+	Signs for the Atkin-Lehner involutions
Class	4028a	Isogeny class
Conductor	4028	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	324	Modular degree for the optimal curve
Δ	-16112 = -1 · 24 · 19 · 53	Discriminant
Eigenvalues	2-  1  2 -4 -3  4  7 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2,-7]	[a1,a2,a3,a4,a6]
Generators	[2:1:1]	Generators of the group modulo torsion
j	-87808/1007	j-invariant
L	4.1991601560987	L(r)(E,1)/r!
Ω	1.6676637573993	Real period
R	0.83932989838179	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16112b1 64448f1 36252l1 100700i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4028a1

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
-	1	2	-4	-3	4	7	-	-8	-6	9	-4	6	-11	4	+	4	-10	-13	-15	0	-8	-4	8	4

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Quadratic twists for elliptic curve 4028a1

-4	8	-3	5	-19
16112b1	64448f1	36252l1	100700i1	76532e1

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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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