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	3	Product of Tamagawa factors cp
deg	1296	Modular degree for the optimal curve
Δ	935693 = 113 · 19 · 37	Discriminant
Eigenvalues	0 -2  0 -4 11- -4  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-153,678]	[a1,a2,a3,a4,a6]
Generators	[-14:16:1] [-12:30:1]	Generators of the group modulo torsion
j	398688256000/935693	j-invariant
L	3.3222367449942	L(r)(E,1)/r!
Ω	2.7989730182231	Real period
R	3.5608454136915	Regulator
r	2	Rank of the group of rational points
S	0.99999999999968	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	123728l1 69597d1 85063d1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 7733d1

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 7733d1

-4	-3	-11
123728l1	69597d1	85063d1

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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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