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	[0,1,1,1,0]	[a1,a2,a3,a4,a6]
j	32768/19	j-invariant
L	0.4532532444961	L(r)(E,1)/r!
Ω	4.0792792004649	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	304e1 1216d1 171b1 475a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 19a3

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

---

Quadratic twists for elliptic curve 19a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73	-79
304e1	1216d1	171b1	475a1	931b1	2299d1	3211a1	5491a1	361b1	10051b1	15979a1	18259a1	26011a1	31939b1	35131c1	41971a1	53371a1	66139a1	70699a1	85291a1	95779k1	101251b1	118579c1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations