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	-33107082931 = -1 · 136 · 193	Discriminant
Eigenvalues	0 -2 -3  1 -3 13+ -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-1577,-26178]	[a1,a2,a3,a4,a6]
Generators	[56:253:1]	Generators of the group modulo torsion
j	-89915392/6859	j-invariant
L	1.3665254793772	L(r)(E,1)/r!
Ω	0.37712949549257	Real period
R	1.8117456943966	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	51376x2 28899c2 80275a2 19a1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3211a2

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 3211a2

-4	-3	5	13	-19
51376x2	28899c2	80275a2	19a1	61009b2

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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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