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	16	Product of Tamagawa factors cp
Δ	23970816 = 210 · 34 · 172	Discriminant
Eigenvalues	2- 3-  2 -4  4  6 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-72,0]	[a1,a2,a3,a4,a6]
j	40873252/23409	j-invariant
L	1.8237015160132	L(r)(E,1)/r!
Ω	1.8237015160132	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	816b2 3264i2 1224c2 10200c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 408b2

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 408b2

-4	8	-3	5	-7	-11	13	17
816b2	3264i2	1224c2	10200c2	19992v2	49368n2	68952o2	6936h2

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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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