Cremona's table of elliptic curves

609 = 3 · 7 · 29

Field	Data	Notes
Atkin-Lehner	3+ 7- 29-	Signs for the Atkin-Lehner involutions
Class	609b	Isogeny class
Conductor	609	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	18418027974129 = 312 · 72 · 294	Discriminant
Eigenvalues	-1 3+ -2 7-  4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-13034,528806]	[a1,a2,a3,a4,a6]
Generators	[-124:569:1]	Generators of the group modulo torsion
j	244883173420511137/18418027974129	j-invariant
L	1.1844590786271	L(r)(E,1)/r!
Ω	0.67424077577527	Real period
R	1.7567301195411	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	9744q4 38976x3 1827b4 15225o3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 609b3

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	-2	2	-4	0	-	-8	-10	-6	12	-8	6	12	-10	-12	-16	2	0	4	-6	-6

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Quadratic twists for elliptic curve 609b3

-4	8	-3	5	-7	-11	13	29
9744q4	38976x3	1827b4	15225o3	4263g4	73689c3	102921e3	17661f3

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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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