Cremona's table of elliptic curves

333 = 3² · 37

Field	Data	Notes
Atkin-Lehner	3+ 37+	Signs for the Atkin-Lehner involutions
Class	333b	Isogeny class
Conductor	333	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-728271 = -1 · 39 · 37	Discriminant
Eigenvalues	1 3+ -2 -4  4 -2 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,12,35]	[a1,a2,a3,a4,a6]
Generators	[2:7:1]	Generators of the group modulo torsion
j	9261/37	j-invariant
L	1.828671038488	L(r)(E,1)/r!
Ω	2.0333288908029	Real period
R	1.7986967546267	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5328j1 21312f1 333c1 8325d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 333b1

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	4	-2	-6	-6	8	6	2	+	0	-10	-12	4	-4	10	-4	-12	-10	10	0	-2	-2

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Quadratic twists for elliptic curve 333b1

-4	8	-3	5	-7	-11	13	17	-19	37
5328j1	21312f1	333c1	8325d1	16317a1	40293d1	56277b1	96237c1	120213d1	12321b1

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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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