Cremona's table of elliptic curves

84 = 2² · 3 · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 7-	Signs for the Atkin-Lehner involutions
Class	84a	Isogeny class
Conductor	84	Conductor
∏ cp	18	Product of Tamagawa factors cp
Δ	1306368 = 28 · 36 · 7	Discriminant
Eigenvalues	2- 3-  0 7- -6  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-28,-28]	[a1,a2,a3,a4,a6]
j	9826000/5103	j-invariant
L	1.0951585545828	L(r)(E,1)/r!
Ω	2.1903171091656	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	336a2 1344d2 252a2 2100c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 84a2

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

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Quadratic twists for elliptic curve 84a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37
336a2	1344d2	252a2	2100c2	588b2	10164p2	14196h2	24276a2	30324c2	44436j2	70644d2	80724j2	114996l2

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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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