Cremona's table of elliptic curves

116865 = 3² · 5 · 7² · 53

Field	Data	Notes
Atkin-Lehner	3- 5+ 7+ 53+	Signs for the Atkin-Lehner involutions
Class	116865m	Isogeny class
Conductor	116865	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	827904	Modular degree for the optimal curve
Δ	-885370099542075 = -1 · 37 · 52 · 78 · 532	Discriminant
Eigenvalues	-2 3- 5+ 7+ -2 -5  4 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-7203,1450804]	[a1,a2,a3,a4,a6]
Generators	[4802:116861:8] [49:-1103:1]	Generators of the group modulo torsion
j	-9834496/210675	j-invariant
L	5.4712884539792	L(r)(E,1)/r!
Ω	0.41907869207309	Real period
R	0.27198991090059	Regulator
r	2	Rank of the group of rational points
S	1.0000000000638	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	38955f1 116865bf1	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 116865m1

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
-2	-	+	+	-2	-5	4	-1	-6	-10	7	-3	0	-9	12	+	-14	-2	-1	-10	9	5	18	6	-2

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Quadratic twists for elliptic curve 116865m1

-3	-7
38955f1	116865bf1

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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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