Cremona's table of elliptic curves

3971 = 11 · 19²

Field	Data	Notes
Atkin-Lehner	11- 19-	Signs for the Atkin-Lehner involutions
Class	3971b	Isogeny class
Conductor	3971	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-517504691 = -1 · 11 · 196	Discriminant
Eigenvalues	2  1  1 -2 11- -4 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-2823140,1824832093]	[a1,a2,a3,a4,a6]
Generators	[954290:830883:1000]	Generators of the group modulo torsion
j	-52893159101157376/11	j-invariant
L	7.5139165566745	L(r)(E,1)/r!
Ω	0.66935096951503	Real period
R	5.6128375836362	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	63536u3 35739r3 99275e3 43681m3	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3971b3

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
2	1	1	-2	-	-4	-2	-	-1	0	-7	-3	8	-6	8	6	-5	12	7	3	4	10	-6	-15	7

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Quadratic twists for elliptic curve 3971b3

-4	-3	5	-11	-19
63536u3	35739r3	99275e3	43681m3	11a2

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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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