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	2	Product of Tamagawa factors cp
Δ	1686616064 = 211 · 77	Discriminant
Eigenvalues	2-  0 -2 7- -4 -2  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-14651,-682570]	[a1,a2,a3,a4,a6]
Generators	[3918:13420:27]	Generators of the group modulo torsion
j	1443468546/7	j-invariant
L	1.6420053998926	L(r)(E,1)/r!
Ω	0.43394317672173	Real period
R	7.5678360116053	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	784c4 3136e3 3528k4 9800d3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 392a3

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 392a3

-4	8	-3	5	-7	-11	13	17
784c4	3136e3	3528k4	9800d3	56a4	47432g4	66248e4	113288v4

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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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