Cremona's table of elliptic curves

33 = 3 · 11

Field	Data	Notes
Atkin-Lehner	3+ 11-	Signs for the Atkin-Lehner involutions
Class	33a	Isogeny class
Conductor	33	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	395307 = 33 · 114	Discriminant
Eigenvalues	1 3+ -2  4 11- -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-146,621]	[a1,a2,a3,a4,a6]
j	347873904937/395307	j-invariant
L	0.74733914774274	L(r)(E,1)/r!
Ω	2.989356590971	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	528h3 2112l3 99b3 825b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 33a3

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
1	+	-2	4	-	-2	-2	0	8	-6	-8	6	-2	0	8	6	-4	6	-4	0	-14	-4	12	-6	2

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Quadratic twists for elliptic curve 33a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61
528h3	2112l3	99b3	825b3	1617j3	363a3	5577d3	9537j3	11913i3	17457a3	27753d4	31713e4	45177a4	55473l4	61017a4	72897a4	92697e4	114873c4	122793a4

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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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