Cremona's table of elliptic curves

9752 = 2³ · 23 · 53

Field	Data	Notes
Atkin-Lehner	2+ 23- 53-	Signs for the Atkin-Lehner involutions
Class	9752b	Isogeny class
Conductor	9752	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-2903697008 = -1 · 24 · 23 · 534	Discriminant
Eigenvalues	2+ -1  0  2  4 -5 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-228,2989]	[a1,a2,a3,a4,a6]
Generators	[-15:53:1]	Generators of the group modulo torsion
j	-82283296000/181481063	j-invariant
L	3.7410542882853	L(r)(E,1)/r!
Ω	1.2684973417313	Real period
R	0.36865018999362	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	19504a1 78016e1 87768h1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 9752b1

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	0	2	4	-5	-6	2	-	1	7	4	7	-4	-1	-	12	-2	4	3	-11	2	-10	-12	-2

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Quadratic twists for elliptic curve 9752b1

-4	8	-3
19504a1	78016e1	87768h1

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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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