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	6820b	Isogeny class
Conductor	6820	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	15004000000 = 28 · 56 · 112 · 31	Discriminant
Eigenvalues	2-  0 5-  2 11-  4  0 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-20047,1092486]	[a1,a2,a3,a4,a6]
Generators	[102:330:1]	Generators of the group modulo torsion
j	3480422102131536/58609375	j-invariant
L	4.5495832536103	L(r)(E,1)/r!
Ω	1.1430072201165	Real period
R	1.3267875517434	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	27280o2 109120d2 61380f2 34100d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6820b2

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
-	0	-	2	-	4	0	-8	-4	-6	-	4	-10	4	10	-12	-12	2	-2	-16	4	8	-12	-10	-2

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Quadratic twists for elliptic curve 6820b2

-4	8	-3	5	-11
27280o2	109120d2	61380f2	34100d2	75020e2

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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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