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	3	Product of Tamagawa factors cp
deg	1	Modular degree for the optimal curve
Δ	-6859 = -1 · 193	Discriminant
Eigenvalues	0 -2  3 -1  3 -4 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-9,-15]	[a1,a2,a3,a4,a6]
j	-89915392/6859	j-invariant
L	0.4532532444961	L(r)(E,1)/r!
Ω	1.3597597334883	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	304e2 1216d2 171b2 475a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 19a1

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 19a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73	-79
304e2	1216d2	171b2	475a2	931b2	2299d2	3211a2	5491a2	361b2	10051b2	15979a2	18259a2	26011a2	31939b2	35131c2	41971a2	53371a2	66139a2	70699a2	85291a2	95779k2	101251b2	118579c2

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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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