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	1	Product of Tamagawa factors cp
deg	20	Modular degree for the optimal curve
Δ	26973 = 36 · 37	Discriminant
Eigenvalues	0 3-  0 -1 -3 -4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-30,-63]	[a1,a2,a3,a4,a6]
Generators	[-3:0:1]	Generators of the group modulo torsion
j	4096000/37	j-invariant
L	1.479299492077	L(r)(E,1)/r!
Ω	2.0410609925639	Real period
R	0.72476986109993	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	5328u1 21312k1 37b3 8325q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 333a1

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 333a1

-4	8	-3	5	-7	-11	13	17	-19	37
5328u1	21312k1	37b3	8325q1	16317g1	40293j1	56277c1	96237e1	120213h1	12321c1

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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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