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	994g	Isogeny class
Conductor	994	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	50215311297032 = 23 · 72 · 716	Discriminant
Eigenvalues	2- -2  0 7- -6  2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-52238,-4587140]	[a1,a2,a3,a4,a6]
Generators	[-130:170:1]	Generators of the group modulo torsion
j	15764632639032390625/50215311297032	j-invariant
L	2.6207661259998	L(r)(E,1)/r!
Ω	0.31585375610137	Real period
R	2.7658012348798	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	7952e4 31808j4 8946i4 24850b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 994g4

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

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Quadratic twists for elliptic curve 994g4

-4	8	-3	5	-7	-11	-71
7952e4	31808j4	8946i4	24850b4	6958n4	120274d4	70574m4

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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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