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	4	Product of Tamagawa factors cp
Δ	36963 = 33 · 372	Discriminant
Eigenvalues	-1 3+  2 -4 -4 -2  6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-14,-14]	[a1,a2,a3,a4,a6]
Generators	[-2:2:1]	Generators of the group modulo torsion
j	10503459/1369	j-invariant
L	1.2023832503028	L(r)(E,1)/r!
Ω	2.5034325770495	Real period
R	0.48029384187369	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	5328i2 21312h2 333b2 8325c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 333c2

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 333c2

-4	8	-3	5	-7	-11	13	17	-19	37
5328i2	21312h2	333b2	8325c2	16317b2	40293b2	56277a2	96237d2	120213c2	12321a2

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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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