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	8	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-4513839183 = -1 · 33 · 78 · 29	Discriminant
Eigenvalues	-1 3+ -2 7-  4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-784,8720]	[a1,a2,a3,a4,a6]
Generators	[-5:114:1]	Generators of the group modulo torsion
j	-53297461115137/4513839183	j-invariant
L	1.1844590786271	L(r)(E,1)/r!
Ω	1.3484815515505	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	9744q1 38976x1 1827b1 15225o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 609b1

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 609b1

-4	8	-3	5	-7	-11	13	29
9744q1	38976x1	1827b1	15225o1	4263g1	73689c1	102921e1	17661f1

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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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