Cremona's table of elliptic curves

759 = 3 · 11 · 23

Field	Data	Notes
Atkin-Lehner	3- 11- 23+	Signs for the Atkin-Lehner involutions
Class	759b	Isogeny class
Conductor	759	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-2584262514273 = -1 · 3 · 11 · 238	Discriminant
Eigenvalues	-1 3- -2  0 11- -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-5654,-181467]	[a1,a2,a3,a4,a6]
Generators	[3362970:25991797:27000]	Generators of the group modulo torsion
j	-19989223566735457/2584262514273	j-invariant
L	1.6306147759645	L(r)(E,1)/r!
Ω	0.27331121034691	Real period
R	11.932293402051	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	12144w6 48576c5 2277b6 18975e6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 759b6

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	0	-	-2	2	-4	+	-2	0	-10	-6	-12	0	14	-4	6	-4	-8	-6	8	4	-14	2

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Quadratic twists for elliptic curve 759b6

-4	8	-3	5	-7	-11	13	-23
12144w6	48576c5	2277b6	18975e6	37191b5	8349c6	128271p5	17457c6

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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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