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	994d	Isogeny class
Conductor	994	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-408575541248 = -1 · 224 · 73 · 71	Discriminant
Eigenvalues	2+  1  0 7- -3 -1 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1611,-39690]	[a1,a2,a3,a4,a6]
Generators	[591:14040:1]	Generators of the group modulo torsion
j	-461979552147625/408575541248	j-invariant
L	2.110157842968	L(r)(E,1)/r!
Ω	0.36340905701106	Real period
R	0.9677606186279	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7952c2 31808n2 8946v2 24850s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 994d2

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
+	1	0	-	-3	-1	-6	-4	3	-9	8	5	3	-4	-12	6	12	-1	8	-	-4	-10	-9	-12	-1

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Quadratic twists for elliptic curve 994d2

-4	8	-3	5	-7	-11	-71
7952c2	31808n2	8946v2	24850s2	6958f2	120274k2	70574a2

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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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