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	490a	Isogeny class
Conductor	490	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	-115296020 = -1 · 22 · 5 · 78	Discriminant
Eigenvalues	2+  1 5+ 7+ -6 -4  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,121,46]	[a1,a2,a3,a4,a6]
Generators	[1:12:1]	Generators of the group modulo torsion
j	34391/20	j-invariant
L	1.5859684246354	L(r)(E,1)/r!
Ω	1.126874966549	Real period
R	2.1111061187547	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	3920p1 15680bg1 4410bj1 2450s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 490a1

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 490a1

-4	8	-3	5	-7	-11	13
3920p1	15680bg1	4410bj1	2450s1	490d1	59290cl1	82810cg1

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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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