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	3822bf	Isogeny class
Conductor	3822	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-66869712 = -1 · 24 · 38 · 72 · 13	Discriminant
Eigenvalues	2- 3-  0 7- -5 13- -7 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-78,468]	[a1,a2,a3,a4,a6]
Generators	[-6:30:1]	Generators of the group modulo torsion
j	-1071912625/1364688	j-invariant
L	5.8184176888342	L(r)(E,1)/r!
Ω	1.7674730319075	Real period
R	0.10287316948754	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	30576by1 122304n1 11466u1 95550ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3822bf1

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	-	-5	-	-7	-7	2	-9	0	4	-4	2	3	1	-7	-13	3	9	10	14	-16	12	-6

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Quadratic twists for elliptic curve 3822bf1

-4	8	-3	5	-7	13
30576by1	122304n1	11466u1	95550ba1	3822r1	49686bd1

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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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