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	408c	Isogeny class
Conductor	408	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-9814051584 = -1 · 28 · 33 · 175	Discriminant
Eigenvalues	2- 3+  3  0 -1  3 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,511,-1899]	[a1,a2,a3,a4,a6]
j	57530252288/38336139	j-invariant
L	1.4687172833518	L(r)(E,1)/r!
Ω	0.73435864167592	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	816d1 3264n1 1224e1 10200q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 408c1

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
-	+	3	0	-1	3	+	1	7	6	-2	-4	9	-1	10	-2	-6	-12	-4	-12	-10	2	-14	4	12

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Quadratic twists for elliptic curve 408c1

-4	8	-3	5	-7	-11	13	17
816d1	3264n1	1224e1	10200q1	19992bb1	49368h1	68952c1	6936n1

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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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