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	-2552757445339983 = -1 · 36 · 7 · 298	Discriminant
Eigenvalues	-1 3+ -2 7-  4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,12481,2376092]	[a1,a2,a3,a4,a6]
Generators	[78:1918:1]	Generators of the group modulo torsion
j	215015459663151503/2552757445339983	j-invariant
L	1.1844590786271	L(r)(E,1)/r!
Ω	0.33712038788764	Real period
R	0.87836505977053	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	9744q6 38976x5 1827b6 15225o6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 609b6

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 609b6

-4	8	-3	5	-7	-11	13	29
9744q6	38976x5	1827b6	15225o6	4263g6	73689c5	102921e5	17661f6

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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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