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	4998bn	Isogeny class
Conductor	4998	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	18816	Modular degree for the optimal curve
Δ	-49787957487744 = -1 · 27 · 34 · 710 · 17	Discriminant
Eigenvalues	2- 3-  3 7-  2  0 17+  3	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-21659,-1274799]	[a1,a2,a3,a4,a6]
j	-3977954113/176256	j-invariant
L	5.4953378642833	L(r)(E,1)/r!
Ω	0.19626206658155	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	39984bw1 14994bk1 124950w1 4998bb1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4998bn1

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	-	2	0	+	3	-5	6	0	3	0	-1	6	-6	-5	-10	-7	3	4	16	12	-5	4

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Quadratic twists for elliptic curve 4998bn1

-4	-3	5	-7	17
39984bw1	14994bk1	124950w1	4998bb1	84966di1

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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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