Cremona's table of elliptic curves

392 = 2³ · 7²

Field	Data	Notes
Atkin-Lehner	2+ 7-	Signs for the Atkin-Lehner involutions
Class	392b	Isogeny class
Conductor	392	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	4519603984 = 24 · 710	Discriminant
Eigenvalues	2+  1  1 7-  3  6  5 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-800,-8359]	[a1,a2,a3,a4,a6]
j	12544	j-invariant
L	1.8042748572037	L(r)(E,1)/r!
Ω	0.90213742860185	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	784d1 3136g1 3528w1 9800be1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 392b1

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	1	-	3	6	5	-1	-7	2	5	3	2	-4	-5	-1	-15	5	-9	0	-7	1	-12	-7	2

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Quadratic twists for elliptic curve 392b1

-4	8	-3	5	-7	-11	13	17
784d1	3136g1	3528w1	9800be1	392c1	47432w1	66248r1	113288h1

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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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