Cremona's table of elliptic curves

608 = 2⁵ · 19

Field	Data	Notes
Atkin-Lehner	2- 19+	Signs for the Atkin-Lehner involutions
Class	608b	Isogeny class
Conductor	608	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-10142101504 = -1 · 212 · 195	Discriminant
Eigenvalues	2-  0  3  5  5 -4 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-56,4848]	[a1,a2,a3,a4,a6]
j	-4741632/2476099	j-invariant
L	2.0861679233631	L(r)(E,1)/r!
Ω	1.0430839616816	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	608e1 1216n1 5472h1 15200b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 608b1

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
-	0	3	5	5	-4	-3	+	0	0	-10	8	0	5	-5	-6	10	-5	10	-10	-11	10	0	-10	-12

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Quadratic twists for elliptic curve 608b1

-4	8	-3	5	-7	-11	13	-19
608e1	1216n1	5472h1	15200b1	29792m1	73568i1	102752e1	11552i1

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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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