Cremona's table of elliptic curves

6409 = 13 · 17 · 29

Field	Data	Notes
Atkin-Lehner	13+ 17- 29+	Signs for the Atkin-Lehner involutions
Class	6409b	Isogeny class
Conductor	6409	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-34544311321 = -1 · 132 · 172 · 294	Discriminant
Eigenvalues	1 -2 -2  2  6 13+ 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,603,-6835]	[a1,a2,a3,a4,a6]
j	24305835707063/34544311321	j-invariant
L	1.2346135680575	L(r)(E,1)/r!
Ω	0.61730678402877	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	102544f2 57681h2 83317f2 108953b2	Quadratic twists by: -4 -3 13 17

Hecke Eigenvalues for elliptic curve 6409b2

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

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Quadratic twists for elliptic curve 6409b2

-4	-3	13	17
102544f2	57681h2	83317f2	108953b2

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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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