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
deg	64	Modular degree for the optimal curve
Δ	39168 = 28 · 32 · 17	Discriminant
Eigenvalues	2- 3-  2 -4  4  6 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-52,128]	[a1,a2,a3,a4,a6]
j	61918288/153	j-invariant
L	1.8237015160132	L(r)(E,1)/r!
Ω	3.6474030320263	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	816b1 3264i1 1224c1 10200c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 408b1

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 408b1

-4	8	-3	5	-7	-11	13	17
816b1	3264i1	1224c1	10200c1	19992v1	49368n1	68952o1	6936h1

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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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