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	2	Product of Tamagawa factors cp
Δ	38367 = 33 · 72 · 29	Discriminant
Eigenvalues	-1 3+ -2 7-  4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-204624,35542050]	[a1,a2,a3,a4,a6]
Generators	[1317:44646:1]	Generators of the group modulo torsion
j	947531277805646290177/38367	j-invariant
L	1.1844590786271	L(r)(E,1)/r!
Ω	1.3484815515505	Real period
R	7.0269204781642	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	9744q3 38976x4 1827b3 15225o4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 609b4

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 609b4

-4	8	-3	5	-7	-11	13	29
9744q3	38976x4	1827b3	15225o4	4263g3	73689c4	102921e4	17661f4

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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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