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	4	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	156672 = 210 · 32 · 17	Discriminant
Eigenvalues	2+ 3-  0  2  0  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-48,-144]	[a1,a2,a3,a4,a6]
j	12194500/153	j-invariant
L	1.8120385465833	L(r)(E,1)/r!
Ω	1.8120385465833	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	816a1 3264b1 1224h1 10200bc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 408a1

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 408a1

-4	8	-3	5	-7	-11	13	17
816a1	3264b1	1224h1	10200bc1	19992f1	49368bh1	68952y1	6936c1

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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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