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	2002a	Isogeny class
Conductor	2002	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2160	Modular degree for the optimal curve
Δ	-310426468352 = -1 · 218 · 72 · 11 · 133	Discriminant
Eigenvalues	2+  0  2 7+ 11+ 13- -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-691,-27531]	[a1,a2,a3,a4,a6]
j	-36518366116233/310426468352	j-invariant
L	1.2264615520686	L(r)(E,1)/r!
Ω	0.40882051735621	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	16016m1 64064d1 18018bi1 50050br1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2002a1

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	+	+	-	-4	0	4	4	4	4	10	4	8	6	6	10	12	-14	-14	-6	0	0	16

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Quadratic twists for elliptic curve 2002a1

-4	8	-3	5	-7	-11	13
16016m1	64064d1	18018bi1	50050br1	14014a1	22022s1	26026q1

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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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