Cremona's table of elliptic curves

2982 = 2 · 3 · 7 · 71

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 71+	Signs for the Atkin-Lehner involutions
Class	2982g	Isogeny class
Conductor	2982	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	358609642272 = 25 · 32 · 72 · 714	Discriminant
Eigenvalues	2- 3+ -2 7-  0  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-75369,-7995465]	[a1,a2,a3,a4,a6]
Generators	[-159:86:1]	Generators of the group modulo torsion
j	47348075501445486097/358609642272	j-invariant
L	3.8859817786492	L(r)(E,1)/r!
Ω	0.28813866107565	Real period
R	1.3486499049251	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	23856ba4 95424bb4 8946j4 74550bc4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2982g3

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	2	-6	-4	0	6	0	-2	2	4	-8	-14	0	-6	8	+	-6	-8	-12	10	2

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Quadratic twists for elliptic curve 2982g3

-4	8	-3	5	-7
23856ba4	95424bb4	8946j4	74550bc4	20874bh4

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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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