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	408a	Isogeny class
Conductor	408	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-47941632 = -1 · 211 · 34 · 172	Discriminant
Eigenvalues	2+ 3-  0  2  0  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-8,-336]	[a1,a2,a3,a4,a6]
j	-31250/23409	j-invariant
L	1.8120385465833	L(r)(E,1)/r!
Ω	0.90601927329166	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	816a2 3264b2 1224h2 10200bc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 408a2

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	0	2	+	4	2	0	6	0	-10	4	-4	-2	-4	0	4	-2	-14	6	-12	-2	-2

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Quadratic twists for elliptic curve 408a2

-4	8	-3	5	-7	-11	13	17
816a2	3264b2	1224h2	10200bc2	19992f2	49368bh2	68952y2	6936c2

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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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