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
deg	96	Modular degree for the optimal curve
Δ	-19120976 = -1 · 24 · 72 · 293	Discriminant
Eigenvalues	2+  1 -3 7- -3 -1  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-15,210]	[a1,a2,a3,a4,a6]
Generators	[3:12:1]	Generators of the group modulo torsion
j	-338608873/19120976	j-invariant
L	1.4272791043686	L(r)(E,1)/r!
Ω	1.7971708524253	Real period
R	0.59563581661247	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	3248k1 12992o1 3654u1 10150i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 406b1

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 406b1

-4	8	-3	5	-7	-11	13	17	29
3248k1	12992o1	3654u1	10150i1	2842d1	49126d1	68614p1	117334a1	11774j1

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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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