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	490d	Isogeny class
Conductor	490	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-392000 = -1 · 26 · 53 · 72	Discriminant
Eigenvalues	2+ -1 5- 7- -6  4  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-32,64]	[a1,a2,a3,a4,a6]
Generators	[8:16:1]	Generators of the group modulo torsion
j	-77626969/8000	j-invariant
L	1.3457322218231	L(r)(E,1)/r!
Ω	2.9268743131282	Real period
R	0.076630794370347	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	3920bd2 15680m2 4410bf2 2450w2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 490d2

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	4	0	-2	-3	-3	-8	-4	-9	-7	0	-6	6	-5	5	-6	16	2	-3	15	-14

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Quadratic twists for elliptic curve 490d2

-4	8	-3	5	-7	-11	13
3920bd2	15680m2	4410bf2	2450w2	490a2	59290ek2	82810bz2

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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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