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	4	Product of Tamagawa factors cp
Δ	1662662681263647 = 324 · 7 · 292	Discriminant
Eigenvalues	-1 3+ -2 7-  4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-42469,-2756140]	[a1,a2,a3,a4,a6]
Generators	[-153:511:1]	Generators of the group modulo torsion
j	8471112631466271697/1662662681263647	j-invariant
L	1.1844590786271	L(r)(E,1)/r!
Ω	0.33712038788764	Real period
R	3.5134602390821	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	9744q5 38976x6 1827b5 15225o5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 609b5

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 609b5

-4	8	-3	5	-7	-11	13	29
9744q5	38976x6	1827b5	15225o5	4263g5	73689c6	102921e6	17661f5

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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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