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	10	Product of Tamagawa factors cp
Δ	-7576786180931 = -1 · 115 · 196	Discriminant
Eigenvalues	2  1  1 -2 11- -4 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-3730,157593]	[a1,a2,a3,a4,a6]
Generators	[-294:3967:8]	Generators of the group modulo torsion
j	-122023936/161051	j-invariant
L	7.5139165566745	L(r)(E,1)/r!
Ω	0.66935096951503	Real period
R	1.1225675167272	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	63536u2 35739r2 99275e2 43681m2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3971b2

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 3971b2

-4	-3	5	-11	-19
63536u2	35739r2	99275e2	43681m2	11a1

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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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