Cremona's table of elliptic curves

208 = 2⁴ · 13

Field	Data	Notes
Atkin-Lehner	2- 13-	Signs for the Atkin-Lehner involutions
Class	208a	Isogeny class
Conductor	208	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-71991296 = -1 · 215 · 133	Discriminant
Eigenvalues	2- -1 -3  1 -6 13- -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-72,496]	[a1,a2,a3,a4,a6]
Generators	[36:208:1]	Generators of the group modulo torsion
j	-10218313/17576	j-invariant
L	1.1571474716311	L(r)(E,1)/r!
Ω	1.7396717417158	Real period
R	0.055429397200047	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	26a1 832g2 1872s2 5200p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 208a2

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
-	-1	-3	1	-6	-	-3	-2	0	6	4	-7	0	1	-3	0	6	8	-14	3	2	-8	-12	-6	-10

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Quadratic twists for elliptic curve 208a2

-4	8	-3	5	-7	-11	13	17	-19	-23
26a1	832g2	1872s2	5200p2	10192u2	25168bb2	2704g2	60112x2	75088t2	110032q2

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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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