Cremona's table of elliptic curves

498 = 2 · 3 · 83

Field	Data	Notes
Atkin-Lehner	2+ 3- 83-	Signs for the Atkin-Lehner involutions
Class	498b	Isogeny class
Conductor	498	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-322704 = -1 · 24 · 35 · 83	Discriminant
Eigenvalues	2+ 3- -1 -4  3 -6 -4 -3	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-9,28]	[a1,a2,a3,a4,a6]
Generators	[-1:6:1]	Generators of the group modulo torsion
j	-68417929/322704	j-invariant
L	1.5703804736827	L(r)(E,1)/r!
Ω	2.6505109414589	Real period
R	0.059248216980322	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	3984b1 15936a1 1494c1 12450m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 498b1

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	-4	3	-6	-4	-3	-1	4	-2	3	6	-12	0	-9	-7	-1	7	0	4	-4	-	5	10

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Quadratic twists for elliptic curve 498b1

-4	8	-3	5	-7	-11	13	-83
3984b1	15936a1	1494c1	12450m1	24402a1	60258z1	84162t1	41334h1

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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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