Cremona's table of elliptic curves

406 = 2 · 7 · 29

Field	Data	Notes
Atkin-Lehner	2+ 7+ 29+	Signs for the Atkin-Lehner involutions
Class	406a	Isogeny class
Conductor	406	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	-295386112 = -1 · 210 · 73 · 292	Discriminant
Eigenvalues	2+  0  0 7+ -4  0 -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-302,2260]	[a1,a2,a3,a4,a6]
Generators	[9:10:1]	Generators of the group modulo torsion
j	-3051779837625/295386112	j-invariant
L	1.3611714716044	L(r)(E,1)/r!
Ω	1.6875693147173	Real period
R	0.80658700044709	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	3248l1 12992f1 3654t1 10150k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 406a1

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	0	+	-4	0	-4	4	0	+	-6	-2	-8	4	2	-2	-10	-2	8	16	0	-4	-6	0	12

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Quadratic twists for elliptic curve 406a1

-4	8	-3	5	-7	-11	13	17	29
3248l1	12992f1	3654t1	10150k1	2842a1	49126h1	68614w1	117334g1	11774f1

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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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