Cremona's table of elliptic curves

116 = 2² · 29

Field	Data	Notes
Atkin-Lehner	2- 29+	Signs for the Atkin-Lehner involutions
Class	116a	Isogeny class
Conductor	116	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	-7424 = -1 · 28 · 29	Discriminant
Eigenvalues	2- -3  3  4 -1 -3  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4831,-129242]	[a1,a2,a3,a4,a6]
j	-48707390098512/29	j-invariant
L	0.85897703766841	L(r)(E,1)/r!
Ω	0.2863256792228	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	464f1 1856g1 1044i1 2900d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 116a1

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
-	-3	3	4	-1	-3	2	4	-6	+	9	-8	-8	-5	-7	-5	-10	10	8	-2	0	-1	6	12	0

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Quadratic twists for elliptic curve 116a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
464f1	1856g1	1044i1	2900d1	5684h1	14036g1	19604c1	33524f1	41876e1	61364c1	3364c1	111476g1

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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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