Cremona's table of elliptic curves

333 = 3² · 37

Field	Data	Notes
Atkin-Lehner	3- 37-	Signs for the Atkin-Lehner involutions
Class	333a	Isogeny class
Conductor	333	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	36926037 = 36 · 373	Discriminant
Eigenvalues	0 3-  0 -1 -3 -4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-210,1134]	[a1,a2,a3,a4,a6]
Generators	[6:9:1]	Generators of the group modulo torsion
j	1404928000/50653	j-invariant
L	1.479299492077	L(r)(E,1)/r!
Ω	2.0410609925639	Real period
R	2.1743095832998	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	5328u2 21312k2 37b1 8325q2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 333a2

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	-	0	-1	-3	-4	-6	2	-6	6	-4	-	9	8	-3	3	-12	8	-4	15	11	-10	-9	-6	8

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Quadratic twists for elliptic curve 333a2

-4	8	-3	5	-7	-11	13	17	-19	37
5328u2	21312k2	37b1	8325q2	16317g2	40293j2	56277c2	96237e2	120213h2	12321c2

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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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