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	1	Product of Tamagawa factors cp
Δ	297 = 33 · 11	Discriminant
Eigenvalues	1 3+ -2  4 11- -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-6,-9]	[a1,a2,a3,a4,a6]
j	30664297/297	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	2	Number of elements in the torsion subgroup
Twists	528h1 2112l1 99b1 825b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 33a2

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 33a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61
528h1	2112l1	99b1	825b1	1617j1	363a1	5577d1	9537j1	11913i1	17457a1	27753d1	31713e1	45177a1	55473l1	61017a1	72897a1	92697e1	114873c1	122793a1

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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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