Cremona's table of elliptic curves

6820 = 2² · 5 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2- 5- 11- 31-	Signs for the Atkin-Lehner involutions
Class	6820c	Isogeny class
Conductor	6820	Conductor
∏ cp	84	Product of Tamagawa factors cp
Δ	16517187500000000 = 28 · 514 · 11 · 312	Discriminant
Eigenvalues	2- -2 5- -4 11-  0 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-82420,6659268]	[a1,a2,a3,a4,a6]
Generators	[256:1550:1]	Generators of the group modulo torsion
j	241872696679049296/64520263671875	j-invariant
L	2.5102282020891	L(r)(E,1)/r!
Ω	0.36518986630447	Real period
R	0.32732199690968	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	27280p2 109120f2 61380i2 34100e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6820c2

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

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Quadratic twists for elliptic curve 6820c2

-4	8	-3	5	-11
27280p2	109120f2	61380i2	34100e2	75020h2

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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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