Cremona's table of elliptic curves

7733 = 11 · 19 · 37

Field	Data	Notes
Atkin-Lehner	11- 19- 37-	Signs for the Atkin-Lehner involutions
Class	7733d	Isogeny class
Conductor	7733	Conductor
∏ cp	9	Product of Tamagawa factors cp
Δ	3821718197 = 11 · 193 · 373	Discriminant
Eigenvalues	0 -2  0 -4 11- -4  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-703,-6769]	[a1,a2,a3,a4,a6]
Generators	[-19:9:1] [-13:18:1]	Generators of the group modulo torsion
j	38477541376000/3821718197	j-invariant
L	3.3222367449942	L(r)(E,1)/r!
Ω	0.93299100607436	Real period
R	0.39564949041016	Regulator
r	2	Rank of the group of rational points
S	0.99999999999968	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	123728l2 69597d2 85063d2	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 7733d2

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
0	-2	0	-4	-	-4	3	-	0	0	-7	-	-3	-1	-9	-12	-9	-10	2	-6	-16	-10	0	-6	-7

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Quadratic twists for elliptic curve 7733d2

-4	-3	-11
123728l2	69597d2	85063d2

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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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