Cremona's table of elliptic curves

392 = 2³ · 7²

Field	Data	Notes
Atkin-Lehner	2- 7-	Signs for the Atkin-Lehner involutions
Class	392f	Isogeny class
Conductor	392	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	784 = 24 · 72	Discriminant
Eigenvalues	2- -3  1 7- -1 -2 -3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7,7]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	48384	j-invariant
L	1.3056845741021	L(r)(E,1)/r!
Ω	5.038029443786	Real period
R	0.12958286455755	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	784f1 3136n1 3528j1 9800m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 392f1

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
-	-3	1	-	-1	-2	-3	-5	-3	-6	1	-5	10	-4	-1	-9	-3	-3	11	16	-7	-11	4	9	-6

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Quadratic twists for elliptic curve 392f1

-4	8	-3	5	-7	-11	13	17
784f1	3136n1	3528j1	9800m1	392e1	47432m1	66248l1	113288bb1

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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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