Cremona's table of elliptic curves

3211 = 13² · 19

Field	Data	Notes
Atkin-Lehner	13+ 19+	Signs for the Atkin-Lehner involutions
Class	3211a	Isogeny class
Conductor	3211	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-91709371 = -1 · 136 · 19	Discriminant
Eigenvalues	0 -2 -3  1 -3 13+ -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-130017,-18088053]	[a1,a2,a3,a4,a6]
Generators	[2773:144748:1]	Generators of the group modulo torsion
j	-50357871050752/19	j-invariant
L	1.3665254793772	L(r)(E,1)/r!
Ω	0.12570983183086	Real period
R	5.4352370831898	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	51376x3 28899c3 80275a3 19a2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3211a3

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	+	-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 3211a3

-4	-3	5	13	-19
51376x3	28899c3	80275a3	19a2	61009b3

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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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