Cremona's table of elliptic curves

19 = Prime conductor

Field	Data	Notes
Atkin-Lehner	19-	Signs for the Atkin-Lehner involutions
Class	19a	Isogeny class
Conductor	19	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-19 = Prime discriminant	Discriminant
Eigenvalues	0 -2  3 -1  3 -4 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-769,-8470]	[a1,a2,a3,a4,a6]
j	-50357871050752/19	j-invariant
L	0.4532532444961	L(r)(E,1)/r!
Ω	0.4532532444961	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	304e3 1216d3 171b3 475a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 19a2

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	-2	3	-1	3	-4	-3	-	0	6	-4	2	-6	-1	-3	12	-6	-1	-4	6	-7	8	12	12	8

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Quadratic twists for elliptic curve 19a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73	-79
304e3	1216d3	171b3	475a3	931b3	2299d3	3211a3	5491a3	361b3	10051b3	15979a3	18259a3	26011a3	31939b3	35131c3	41971a3	53371a3	66139a3	70699a3	85291a3	95779k3	101251b3	118579c3

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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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