Cremona's table of elliptic curves

3822 = 2 · 3 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 13-	Signs for the Atkin-Lehner involutions
Class	3822bg	Isogeny class
Conductor	3822	Conductor
∏ cp	2380	Product of Tamagawa factors cp
deg	228480	Modular degree for the optimal curve
Δ	-8.7651984035481E+19	Discriminant
Eigenvalues	2- 3- -3 7-  1 13- -7 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-4923717,4228856001]	[a1,a2,a3,a4,a6]
Generators	[1656:-25671:1]	Generators of the group modulo torsion
j	-112205650221491190337/745029571313664	j-invariant
L	5.2321504946238	L(r)(E,1)/r!
Ω	0.19231700741972	Real period
R	0.011431035612823	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	30576cg1 122304be1 11466be1 95550n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3822bg1

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
-	-	-3	-	1	-	-7	-1	-7	3	0	-5	-4	11	0	-14	-4	-1	-6	-12	-5	-10	14	6	-6

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Quadratic twists for elliptic curve 3822bg1

-4	8	-3	5	-7	13
30576cg1	122304be1	11466be1	95550n1	546e1	49686bl1

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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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