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	406c	Isogeny class
Conductor	406	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	-363776 = -1 · 28 · 72 · 29	Discriminant
Eigenvalues	2- -1 -3 7+ -1 -1 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-102,355]	[a1,a2,a3,a4,a6]
Generators	[7:-11:1]	Generators of the group modulo torsion
j	-117433042273/363776	j-invariant
L	1.9468317637391	L(r)(E,1)/r!
Ω	3.0327084838015	Real period
R	0.040121556649314	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	3248n1 12992b1 3654i1 10150e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 406c1

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	-3	+	-1	-1	-4	-4	-2	-	-1	6	0	3	-9	3	0	6	2	-8	0	-13	0	-14	16

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Quadratic twists for elliptic curve 406c1

-4	8	-3	5	-7	-11	13	17	29
3248n1	12992b1	3654i1	10150e1	2842f1	49126c1	68614h1	117334o1	11774b1

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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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