Cremona's table of elliptic curves

82 = 2 · 41

Field	Data	Notes
Atkin-Lehner	2+ 41+	Signs for the Atkin-Lehner involutions
Class	82a	Isogeny class
Conductor	82	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	3362 = 2 · 412	Discriminant
Eigenvalues	2+ -2 -2 -4 -2  4 -2  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-12,-16]	[a1,a2,a3,a4,a6]
Generators	[-2:1:1]	Generators of the group modulo torsion
j	169112377/3362	j-invariant
L	0.58300155947061	L(r)(E,1)/r!
Ω	2.5944975201858	Real period
R	0.44941384983776	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	656c2 2624b2 738i2 2050e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 82a2

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

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Quadratic twists for elliptic curve 82a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41
656c2	2624b2	738i2	2050e2	4018f2	9922d2	13858m2	23698d2	29602g2	43378d2	68962k2	78802a2	112258d2	3362b2

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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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