Cremona's table of elliptic curves

8214 = 2 · 3 · 37²

Field	Data	Notes
Atkin-Lehner	2- 3- 37+	Signs for the Atkin-Lehner involutions
Class	8214j	Isogeny class
Conductor	8214	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-2299394304 = -1 · 28 · 38 · 372	Discriminant
Eigenvalues	2- 3- -1  2  2 -6 -3  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,64,2304]	[a1,a2,a3,a4,a6]
Generators	[-8:40:1]	Generators of the group modulo torsion
j	21156119/1679616	j-invariant
L	7.3818432457611	L(r)(E,1)/r!
Ω	1.113798029882	Real period
R	0.10355674693304	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	65712r1 24642e1 8214e1	Quadratic twists by: -4 -3 37

Hecke Eigenvalues for elliptic curve 8214j1

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
-	-	-1	2	2	-6	-3	2	-8	-1	-2	+	-9	-10	2	-2	-12	-1	2	6	-2	10	0	1	17

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Quadratic twists for elliptic curve 8214j1

-4	-3	37
65712r1	24642e1	8214e1

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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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