Cremona's table of elliptic curves

2002 = 2 · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 7- 11- 13-	Signs for the Atkin-Lehner involutions
Class	2002b	Isogeny class
Conductor	2002	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	8796788 = 22 · 7 · 11 · 134	Discriminant
Eigenvalues	2+  0  2 7- 11- 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1646,-25296]	[a1,a2,a3,a4,a6]
j	493357359497913/8796788	j-invariant
L	1.4990295361451	L(r)(E,1)/r!
Ω	0.74951476807256	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16016g3 64064k4 18018bo3 50050bj4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2002b3

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	-	-	-	2	-4	0	6	8	6	2	8	0	-10	4	-2	4	8	10	4	4	-2	-18

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Quadratic twists for elliptic curve 2002b3

-4	8	-3	5	-7	-11	13
16016g3	64064k4	18018bo3	50050bj4	14014d3	22022m4	26026i4

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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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