Cremona's table of elliptic curves

4998 = 2 · 3 · 7² · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 17-	Signs for the Atkin-Lehner involutions
Class	4998ba	Isogeny class
Conductor	4998	Conductor
∏ cp	198	Product of Tamagawa factors cp
deg	1330560	Modular degree for the optimal curve
Δ	-8.1936504988658E+24	Discriminant
Eigenvalues	2- 3+  1 7+ -6  0 17- -3	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,9212930,137302547003]	[a1,a2,a3,a4,a6]
Generators	[7127:-755253:1]	Generators of the group modulo torsion
j	15001431500460925919/1421324083670155776	j-invariant
L	4.9096029202805	L(r)(E,1)/r!
Ω	0.056465673931187	Real period
R	0.43913359424469	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	39984cw1 14994n1 124950ck1 4998bk1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4998ba1

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	+	-6	0	-	-3	7	6	-8	7	0	-9	-6	2	-11	-6	9	-9	-12	-8	4	5	-4

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Quadratic twists for elliptic curve 4998ba1

-4	-3	5	-7	17
39984cw1	14994n1	124950ck1	4998bk1	84966dn1

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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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