Cremona's table of elliptic curves

490 = 2 · 5 · 7²

Field	Data	Notes
Atkin-Lehner	2- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	490g	Isogeny class
Conductor	490	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	6860000 = 25 · 54 · 73	Discriminant
Eigenvalues	2- -2 5+ 7- -4 -2 -8  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1191,15721]	[a1,a2,a3,a4,a6]
Generators	[26:-63:1]	Generators of the group modulo torsion
j	544737993463/20000	j-invariant
L	1.9926925955003	L(r)(E,1)/r!
Ω	2.2143485488254	Real period
R	0.17998003038477	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3920w2 15680bu2 4410s2 2450g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 490g2

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	-8	6	-4	-6	-4	-10	-4	4	-4	10	14	10	-4	12	-4	4	2	-8	0

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Quadratic twists for elliptic curve 490g2

-4	8	-3	5	-7	-11	13
3920w2	15680bu2	4410s2	2450g2	490j2	59290z2	82810bl2

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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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