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	32	Product of Tamagawa factors cp
Δ	627352209 = 34 · 114 · 232	Discriminant
Eigenvalues	-1 3- -2  0 11- -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-374,-2541]	[a1,a2,a3,a4,a6]
Generators	[34:139:1]	Generators of the group modulo torsion
j	5786435182177/627352209	j-invariant
L	1.6306147759645	L(r)(E,1)/r!
Ω	1.0932448413876	Real period
R	2.9830733505129	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	12144w2 48576c2 2277b2 18975e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 759b2

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 759b2

-4	8	-3	5	-7	-11	13	-23
12144w2	48576c2	2277b2	18975e2	37191b2	8349c2	128271p2	17457c2

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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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