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	16	Product of Tamagawa factors cp
Δ	44372288367 = 32 · 118 · 23	Discriminant
Eigenvalues	-1 3- -2  0 11- -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1409,17538]	[a1,a2,a3,a4,a6]
Generators	[-41:103:1]	Generators of the group modulo torsion
j	309368403125137/44372288367	j-invariant
L	1.6306147759645	L(r)(E,1)/r!
Ω	1.0932448413876	Real period
R	1.4915366752564	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	12144w3 48576c3 2277b3 18975e4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 759b4

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 759b4

-4	8	-3	5	-7	-11	13	-23
12144w3	48576c3	2277b3	18975e4	37191b3	8349c3	128271p3	17457c3

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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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