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
deg	384	Modular degree for the optimal curve
Δ	-641376512 = -1 · 28 · 7 · 713	Discriminant
Eigenvalues	2+  1  0 7- -3 -1 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,164,922]	[a1,a2,a3,a4,a6]
Generators	[65:503:1]	Generators of the group modulo torsion
j	492103442375/641376512	j-invariant
L	2.110157842968	L(r)(E,1)/r!
Ω	1.0902271710332	Real period
R	2.9032818558837	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	7952c1 31808n1 8946v1 24850s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 994d1

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 994d1

-4	8	-3	5	-7	-11	-71
7952c1	31808n1	8946v1	24850s1	6958f1	120274k1	70574a1

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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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