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
deg	16	Modular degree for the optimal curve
Δ	-106496 = -1 · 213 · 13	Discriminant
Eigenvalues	2- -1 -3  1 -6 13- -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,8,-16]	[a1,a2,a3,a4,a6]
Generators	[4:8:1]	Generators of the group modulo torsion
j	12167/26	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	26a3 832g1 1872s1 5200p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 208a1

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 208a1

-4	8	-3	5	-7	-11	13	17	-19	-23
26a3	832g1	1872s1	5200p1	10192u1	25168bb1	2704g1	60112x1	75088t1	110032q1

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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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