Cremona's table of elliptic curves

608 = 2⁵ · 19

Field	Data	Notes
Atkin-Lehner	2- 19+	Signs for the Atkin-Lehner involutions
Class	608c	Isogeny class
Conductor	608	Conductor
∏ cp	1	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]
j	27000/19	j-invariant
L	2.5878393778152	L(r)(E,1)/r!
Ω	2.5878393778152	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	608f1 1216r1 5472c1 15200c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 608c1

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 608c1

-4	8	-3	5	-7	-11	13	-19
608f1	1216r1	5472c1	15200c1	29792p1	73568l1	102752g1	11552m1

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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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