Cremona's table of elliptic curves

408 = 2³ · 3 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 17-	Signs for the Atkin-Lehner involutions
Class	408b	Isogeny class
Conductor	408	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	228427776 = 211 · 38 · 17	Discriminant
Eigenvalues	2- 3-  2 -4  4  6 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-752,-8160]	[a1,a2,a3,a4,a6]
j	22994537186/111537	j-invariant
L	1.8237015160132	L(r)(E,1)/r!
Ω	0.91185075800658	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	816b3 3264i3 1224c3 10200c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 408b3

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
-	-	2	-4	4	6	-	4	-4	-6	-4	10	-6	4	-8	6	-4	-14	-12	-12	10	-4	4	-6	-6

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Quadratic twists for elliptic curve 408b3

-4	8	-3	5	-7	-11	13	17
816b3	3264i3	1224c3	10200c3	19992v3	49368n4	68952o4	6936h3

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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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