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	406b	Isogeny class
Conductor	406	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-13974818816 = -1 · 212 · 76 · 29	Discriminant
Eigenvalues	2+  1 -3 7- -3 -1  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,130,-5648]	[a1,a2,a3,a4,a6]
Generators	[37:205:1]	Generators of the group modulo torsion
j	245667233447/13974818816	j-invariant
L	1.4272791043686	L(r)(E,1)/r!
Ω	0.59905695080844	Real period
R	0.19854527220416	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	3248k2 12992o2 3654u2 10150i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 406b2

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	-	-3	-1	0	-4	-6	-	5	2	0	-7	-3	-9	12	-10	2	-12	8	5	12	6	8

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Quadratic twists for elliptic curve 406b2

-4	8	-3	5	-7	-11	13	17	29
3248k2	12992o2	3654u2	10150i2	2842d2	49126d2	68614p2	117334a2	11774j2

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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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