Cremona's table of elliptic curves

994 = 2 · 7 · 71

Field	Data	Notes
Atkin-Lehner	2- 7- 71+	Signs for the Atkin-Lehner involutions
Class	994f	Isogeny class
Conductor	994	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	681884 = 22 · 74 · 71	Discriminant
Eigenvalues	2-  0 -2 7- -4 -6  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1516,23091]	[a1,a2,a3,a4,a6]
Generators	[133:1403:1]	Generators of the group modulo torsion
j	385081556901777/681884	j-invariant
L	3.0834509733287	L(r)(E,1)/r!
Ω	2.4540446204528	Real period
R	2.5129542858596	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	7952d3 31808g4 8946k3 24850a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 994f3

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	-6	6	0	-8	-2	0	6	-10	-4	8	-2	12	10	-12	+	-6	-8	-16	2	14

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Quadratic twists for elliptic curve 994f3

-4	8	-3	5	-7	-11	-71
7952d3	31808g4	8946k3	24850a4	6958k3	120274a4	70574l4

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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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