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	3822bb	Isogeny class
Conductor	3822	Conductor
∏ cp	192	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-165691588608 = -1 · 216 · 34 · 74 · 13	Discriminant
Eigenvalues	2- 3- -4 7+ -1 13+  3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3725,89361]	[a1,a2,a3,a4,a6]
Generators	[130:-1409:1]	Generators of the group modulo torsion
j	-2380771254001/69009408	j-invariant
L	4.9541559844002	L(r)(E,1)/r!
Ω	1.0165693250407	Real period
R	0.025382327713902	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	30576bk1 122304g1 11466l1 95550d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3822bb1

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
-	-	-4	+	-1	+	3	-1	6	-9	-8	-8	0	10	-11	1	-5	-15	-5	-15	2	-2	-8	0	10

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Quadratic twists for elliptic curve 3822bb1

-4	8	-3	5	-7	13
30576bk1	122304g1	11466l1	95550d1	3822z1	49686ba1

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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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