Cremona's table of elliptic curves

3330 = 2 · 3² · 5 · 37

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 37+	Signs for the Atkin-Lehner involutions
Class	3330u	Isogeny class
Conductor	3330	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	-2427570 = -1 · 2 · 38 · 5 · 37	Discriminant
Eigenvalues	2- 3- 5-  1  1  2  7 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,13,69]	[a1,a2,a3,a4,a6]
j	357911/3330	j-invariant
L	3.7827724707138	L(r)(E,1)/r!
Ω	1.8913862353569	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	26640bn1 106560bt1 1110a1 16650u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3330u1

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	1	2	7	-2	0	-9	7	+	11	-11	-8	11	10	-1	-8	0	4	12	6	-6	-19

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Quadratic twists for elliptic curve 3330u1

-4	8	-3	5	37
26640bn1	106560bt1	1110a1	16650u1	123210y1

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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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