Cremona's table of elliptic curves

116487 = 3² · 7 · 43²

Field	Data	Notes
Atkin-Lehner	3- 7- 43+	Signs for the Atkin-Lehner involutions
Class	116487i	Isogeny class
Conductor	116487	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	50688	Modular degree for the optimal curve
Δ	-1217172663 = -1 · 37 · 7 · 433	Discriminant
Eigenvalues	-1 3-  0 7- -2 -6  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,40,-1686]	[a1,a2,a3,a4,a6]
Generators	[12:14:1]	Generators of the group modulo torsion
j	125/21	j-invariant
L	4.3864569352244	L(r)(E,1)/r!
Ω	0.72513740363482	Real period
R	3.0245694707144	Regulator
r	1	Rank of the group of rational points
S	1.0000000066136	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	38829c1 116487f1	Quadratic twists by: -3 -43

Hecke Eigenvalues for elliptic curve 116487i1

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	-6	6	4	6	10	2	-4	10	+	0	6	-12	-10	-4	16	6	0	12	-12	-14

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Quadratic twists for elliptic curve 116487i1

-3	-43
38829c1	116487f1

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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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