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	168	Product of Tamagawa factors cp
deg	26880	Modular degree for the optimal curve
Δ	139682551250000 = 24 · 57 · 112 · 314	Discriminant
Eigenvalues	2- -2 5- -4 11-  0 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-29565,-1882100]	[a1,a2,a3,a4,a6]
Generators	[-85:155:1]	Generators of the group modulo torsion
j	178629041914249216/8730159453125	j-invariant
L	2.5102282020891	L(r)(E,1)/r!
Ω	0.36518986630447	Real period
R	0.16366099845484	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	27280p1 109120f1 61380i1 34100e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6820c1

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 6820c1

-4	8	-3	5	-11
27280p1	109120f1	61380i1	34100e1	75020h1

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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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