Cremona's table of elliptic curves

333 = 3² · 37

Field	Data	Notes
Atkin-Lehner	3- 37+	Signs for the Atkin-Lehner involutions
Class	333d	Isogeny class
Conductor	333	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	28	Modular degree for the optimal curve
Δ	26973 = 36 · 37	Discriminant
Eigenvalues	2 3-  2 -1  5 -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-9,-7]	[a1,a2,a3,a4,a6]
j	110592/37	j-invariant
L	2.8306206391573	L(r)(E,1)/r!
Ω	2.8306206391573	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5328q1 21312x1 37a1 8325x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 333d1

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
2	-	2	-1	5	-2	0	0	-2	-6	-4	+	9	2	9	-1	-8	-8	8	-9	-1	4	15	-4	4

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Quadratic twists for elliptic curve 333d1

-4	8	-3	5	-7	-11	13	17	-19	37
5328q1	21312x1	37a1	8325x1	16317f1	40293i1	56277p1	96237o1	120213l1	12321f1

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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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