Cremona's table of elliptic curves

290 = 2 · 5 · 29

Field	Data	Notes
Atkin-Lehner	2+ 5+ 29+	Signs for the Atkin-Lehner involutions
Class	290a	Isogeny class
Conductor	290	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	928000 = 28 · 53 · 29	Discriminant
Eigenvalues	2+  0 5+ -2  2 -6  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-70,-204]	[a1,a2,a3,a4,a6]
Generators	[-5:4:1]	Generators of the group modulo torsion
j	38238692409/928000	j-invariant
L	1.1736436287904	L(r)(E,1)/r!
Ω	1.6518740857378	Real period
R	1.4209843703264	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	2320e1 9280h1 2610n1 1450e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 290a1

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
+	0	+	-2	2	-6	2	-2	-6	+	-6	-2	10	-8	-4	10	8	10	2	4	6	-10	-6	-6	6

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Quadratic twists for elliptic curve 290a1

-4	8	-3	5	-7	-11	13	17	-19	29
2320e1	9280h1	2610n1	1450e1	14210g1	35090s1	49010q1	83810m1	104690bb1	8410g1

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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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