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	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	256256 = 28 · 7 · 11 · 13	Discriminant
Eigenvalues	2+  0  2 7- 11- 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-26,52]	[a1,a2,a3,a4,a6]
j	1986121593/256256	j-invariant
L	1.4990295361451	L(r)(E,1)/r!
Ω	2.9980590722903	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	16016g1 64064k1 18018bo1 50050bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2002b1

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 2002b1

-4	8	-3	5	-7	-11	13
16016g1	64064k1	18018bo1	50050bj1	14014d1	22022m1	26026i1

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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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