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	16	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-210827008 = -1 · 28 · 77	Discriminant
Eigenvalues	2-  0 -2 7- -4 -2  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,49,-686]	[a1,a2,a3,a4,a6]
Generators	[9:22:1]	Generators of the group modulo torsion
j	432/7	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	4	Number of elements in the torsion subgroup
Twists	784c1 3136e1 3528k1 9800d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 392a1

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 392a1

-4	8	-3	5	-7	-11	13	17
784c1	3136e1	3528k1	9800d1	56a1	47432g1	66248e1	113288v1

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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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