Cremona's table of elliptic curves

333 = 3² · 37

Field	Data	Notes
Atkin-Lehner	3+ 37+	Signs for the Atkin-Lehner involutions
Class	333c	Isogeny class
Conductor	333	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-999 = -1 · 33 · 37	Discriminant
Eigenvalues	-1 3+  2 -4 -4 -2  6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,1,-2]	[a1,a2,a3,a4,a6]
Generators	[2:1:1]	Generators of the group modulo torsion
j	9261/37	j-invariant
L	1.2023832503028	L(r)(E,1)/r!
Ω	2.5034325770495	Real period
R	0.96058768374738	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	5328i1 21312h1 333b1 8325c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 333c1

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 333c1

-4	8	-3	5	-7	-11	13	17	-19	37
5328i1	21312h1	333b1	8325c1	16317b1	40293b1	56277a1	96237d1	120213c1	12321a1

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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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