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	4998bm	Isogeny class
Conductor	4998	Conductor
∏ cp	768	Product of Tamagawa factors cp
Δ	6.4997422544797E+22	Discriminant
Eigenvalues	2- 3-  2 7-  4  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-42093157,104393523905]	[a1,a2,a3,a4,a6]
j	70108386184777836280897/552468975892674624	j-invariant
L	5.3208029247745	L(r)(E,1)/r!
Ω	0.1108500609328	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	39984bv4 14994bi3 124950ba4 714g3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4998bm3

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	+	-4	8	6	0	-2	-10	-4	0	6	4	-6	-12	-8	6	0	12	6	-2

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Quadratic twists for elliptic curve 4998bm3

-4	-3	5	-7	17
39984bv4	14994bi3	124950ba4	714g3	84966da4

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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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