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	8	Product of Tamagawa factors cp
Δ	304746849 = 32 · 112 · 234	Discriminant
Eigenvalues	-1 3- -2  0 11- -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-5819,-171336]	[a1,a2,a3,a4,a6]
Generators	[998:7691:8]	Generators of the group modulo torsion
j	21790813729717297/304746849	j-invariant
L	1.6306147759645	L(r)(E,1)/r!
Ω	0.54662242069381	Real period
R	5.9661467010257	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	12144w4 48576c4 2277b4 18975e3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 759b3

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 759b3

-4	8	-3	5	-7	-11	13	-23
12144w4	48576c4	2277b4	18975e3	37191b4	8349c4	128271p4	17457c4

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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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