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	4	Product of Tamagawa factors cp
Δ	-711527068 = -1 · 22 · 7 · 714	Discriminant
Eigenvalues	2-  0 -2 7- -4 -6  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,44,1267]	[a1,a2,a3,a4,a6]
Generators	[-7:27:1]	Generators of the group modulo torsion
j	9622822383/711527068	j-invariant
L	3.0834509733287	L(r)(E,1)/r!
Ω	1.2270223102264	Real period
R	2.5129542858596	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7952d4 31808g3 8946k4 24850a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 994f4

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 994f4

-4	8	-3	5	-7	-11	-71
7952d4	31808g3	8946k4	24850a3	6958k4	120274a3	70574l3

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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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