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	994b	Isogeny class
Conductor	994	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	80222970716 = 22 · 710 · 71	Discriminant
Eigenvalues	2+ -2  2 7+  4  0 -4  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1165,-7044]	[a1,a2,a3,a4,a6]
j	174648757219273/80222970716	j-invariant
L	0.85383006797517	L(r)(E,1)/r!
Ω	0.85383006797517	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	7952h2 31808e2 8946s2 24850y2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 994b2

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

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Quadratic twists for elliptic curve 994b2

-4	8	-3	5	-7	-11	-71
7952h2	31808e2	8946s2	24850y2	6958h2	120274t2	70574j2

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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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