Cremona's table of elliptic curves

392 = 2³ · 7²

Field	Data	Notes
Atkin-Lehner	2- 7-	Signs for the Atkin-Lehner involutions
Class	392a	Isogeny class
Conductor	392	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	578509309952 = 211 · 710	Discriminant
Eigenvalues	2-  0 -2 7- -4 -2  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2891,47334]	[a1,a2,a3,a4,a6]
Generators	[14:98:1]	Generators of the group modulo torsion
j	11090466/2401	j-invariant
L	1.6420053998926	L(r)(E,1)/r!
Ω	0.86788635344347	Real period
R	1.8919590029013	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	784c3 3136e4 3528k3 9800d4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 392a4

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	-2	-	-4	-2	6	-8	0	6	-8	-2	-2	-4	8	6	0	6	-4	-8	-10	16	-8	6	6

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Quadratic twists for elliptic curve 392a4

-4	8	-3	5	-7	-11	13	17
784c3	3136e4	3528k3	9800d4	56a3	47432g3	66248e3	113288v3

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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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