Cremona's table of elliptic curves

4002 = 2 · 3 · 23 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3+ 23- 29+	Signs for the Atkin-Lehner involutions
Class	4002c	Isogeny class
Conductor	4002	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-11141568 = -1 · 26 · 32 · 23 · 292	Discriminant
Eigenvalues	2+ 3+ -2 -2 -4 -2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-231,1269]	[a1,a2,a3,a4,a6]
Generators	[-10:57:1] [6:9:1]	Generators of the group modulo torsion
j	-1372441819897/11141568	j-invariant
L	2.6732310581061	L(r)(E,1)/r!
Ω	2.2833079106407	Real period
R	0.58538558151745	Regulator
r	2	Rank of the group of rational points
S	0.99999999999947	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32016ba1 128064bq1 12006m1 100050cc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002c1

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

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Quadratic twists for elliptic curve 4002c1

-4	8	-3	5	-23	29
32016ba1	128064bq1	12006m1	100050cc1	92046b1	116058be1

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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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