Cremona's table of elliptic curves

608 = 2⁵ · 19

Field	Data	Notes
Atkin-Lehner	2- 19-	Signs for the Atkin-Lehner involutions
Class	608f	Isogeny class
Conductor	608	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-9728 = -1 · 29 · 19	Discriminant
Eigenvalues	2- -3  0  1 -2 -1  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,5,-2]	[a1,a2,a3,a4,a6]
Generators	[1:2:1]	Generators of the group modulo torsion
j	27000/19	j-invariant
L	1.4518436126519	L(r)(E,1)/r!
Ω	2.3045386410347	Real period
R	0.31499658690905	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	608c1 1216m1 5472j1 15200g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 608f1

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	-2	-1	3	-	-3	3	-8	-10	-12	-8	8	-9	5	10	-7	10	1	14	-6	-4	-6

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Quadratic twists for elliptic curve 608f1

-4	8	-3	5	-7	-11	13	-19
608c1	1216m1	5472j1	15200g1	29792l1	73568h1	102752d1	11552k1

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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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