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
deg	6	Modular degree for the optimal curve
Δ	-2352 = -1 · 24 · 3 · 72	Discriminant
Eigenvalues	2- 3+  4 7+  2 -6 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1,-2]	[a1,a2,a3,a4,a6]
j	-16384/147	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	336f1 1344i1 252b1 2100n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 84b1

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 84b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37
336f1	1344i1	252b1	2100n1	588f1	10164o1	14196f1	24276m1	30324i1	44436h1	70644i1	80724p1	114996e1

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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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