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	988b	Isogeny class
Conductor	988	Conductor
∏ cp	39	Product of Tamagawa factors cp
deg	13260	Modular degree for the optimal curve
Δ	-8747020560149468272 = -1 · 24 · 13 · 1913	Discriminant
Eigenvalues	2-  0  2 -2 -2 13+ -7 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-362249,165197113]	[a1,a2,a3,a4,a6]
Generators	[18309:2476099:1]	Generators of the group modulo torsion
j	-328568038616615609088/546688785009341767	j-invariant
L	2.4883343573445	L(r)(E,1)/r!
Ω	0.20759221806041	Real period
R	0.3073498884315	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	3952c1 15808g1 8892j1 24700j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 988b1

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
-	0	2	-2	-2	+	-7	-	-5	2	-3	7	7	-9	-2	6	3	11	-3	-16	2	-4	-6	-6	-11

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Quadratic twists for elliptic curve 988b1

-4	8	-3	5	-7	-11	13	-19
3952c1	15808g1	8892j1	24700j1	48412k1	119548g1	12844a1	18772f1

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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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