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	6	Product of Tamagawa factors cp
Δ	790272 = 28 · 32 · 73	Discriminant
Eigenvalues	2- 3-  0 7- -6  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1828,-30700]	[a1,a2,a3,a4,a6]
j	2640279346000/3087	j-invariant
L	1.0951585545828	L(r)(E,1)/r!
Ω	0.7301057030552	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	336a4 1344d4 252a4 2100c4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 84a4

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 84a4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37
336a4	1344d4	252a4	2100c4	588b4	10164p4	14196h4	24276a4	30324c4	44436j4	70644d4	80724j4	114996l4

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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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