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	4	Product of Tamagawa factors cp
Δ	-27262976 = -1 · 221 · 13	Discriminant
Eigenvalues	2- -1 -3  1 -6 13- -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7352,245104]	[a1,a2,a3,a4,a6]
Generators	[60:128:1]	Generators of the group modulo torsion
j	-10730978619193/6656	j-invariant
L	1.1571474716311	L(r)(E,1)/r!
Ω	1.7396717417158	Real period
R	0.16628819160014	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	26a2 832g3 1872s3 5200p3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 208a3

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 208a3

-4	8	-3	5	-7	-11	13	17	-19	-23
26a2	832g3	1872s3	5200p3	10192u3	25168bb3	2704g3	60112x3	75088t3	110032q3

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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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