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	3330g	Isogeny class
Conductor	3330	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	13810176000 = 212 · 36 · 53 · 37	Discriminant
Eigenvalues	2+ 3- 5+  2  0  2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-675,3861]	[a1,a2,a3,a4,a6]
Generators	[-3:78:1]	Generators of the group modulo torsion
j	46694890801/18944000	j-invariant
L	2.5896385841142	L(r)(E,1)/r!
Ω	1.1381830565221	Real period
R	2.2752390920555	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	26640bg1 106560cp1 370d1 16650bz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3330g1

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	0	2	-6	2	0	-6	-10	-	6	-4	6	-6	6	-10	2	0	2	-10	6	6	2

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Quadratic twists for elliptic curve 3330g1

-4	8	-3	5	37
26640bg1	106560cp1	370d1	16650bz1	123210dj1

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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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