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	84b	Isogeny class
Conductor	84	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	16128 = 28 · 32 · 7	Discriminant
Eigenvalues	2- 3+  4 7+  2 -6 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-36,-72]	[a1,a2,a3,a4,a6]
j	20720464/63	j-invariant
L	0.97246197526711	L(r)(E,1)/r!
Ω	1.9449239505342	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	336f2 1344i2 252b2 2100n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 84b2

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

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Quadratic twists for elliptic curve 84b2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37
336f2	1344i2	252b2	2100n2	588f2	10164o2	14196f2	24276m2	30324i2	44436h2	70644i2	80724p2	114996e2

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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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