Cremona's table of elliptic curves

3306 = 2 · 3 · 19 · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 19+ 29-	Signs for the Atkin-Lehner involutions
Class	3306g	Isogeny class
Conductor	3306	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	1725732 = 22 · 33 · 19 · 292	Discriminant
Eigenvalues	2- 3+ -4  0  0  4 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-30,-9]	[a1,a2,a3,a4,a6]
Generators	[-3:9:1]	Generators of the group modulo torsion
j	2992209121/1725732	j-invariant
L	3.5045823093124	L(r)(E,1)/r!
Ω	2.2581095877549	Real period
R	1.5519983300708	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	26448v1 105792y1 9918g1 82650q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3306g1

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
-	+	-4	0	0	4	-4	+	4	-	2	2	-2	-4	-6	-10	-4	10	2	0	-14	-14	-2	-10	-8

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Quadratic twists for elliptic curve 3306g1

-4	8	-3	5	-19	29
26448v1	105792y1	9918g1	82650q1	62814g1	95874g1

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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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