Cremona's table of elliptic curves

988 = 2² · 13 · 19

Field	Data	Notes
Atkin-Lehner	2- 13+ 19+	Signs for the Atkin-Lehner involutions
Class	988a	Isogeny class
Conductor	988	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	420	Modular degree for the optimal curve
Δ	-112873072 = -1 · 24 · 135 · 19	Discriminant
Eigenvalues	2-  2  4  2  0 13+ -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,114,-247]	[a1,a2,a3,a4,a6]
j	10150866176/7054567	j-invariant
L	3.175209353626	L(r)(E,1)/r!
Ω	1.0584031178753	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	3952h1 15808n1 8892g1 24700h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 988a1

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	4	2	0	+	-3	+	3	-2	-11	-5	-5	11	-6	-14	11	7	-7	12	4	-2	-2	2	17

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Quadratic twists for elliptic curve 988a1

-4	8	-3	5	-7	-11	13	-19
3952h1	15808n1	8892g1	24700h1	48412r1	119548n1	12844e1	18772i1

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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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