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	3822m	Isogeny class
Conductor	3822	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	300557422174464 = 28 · 310 · 76 · 132	Discriminant
Eigenvalues	2+ 3- -2 7- -4 13+ -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-63677,-6133480]	[a1,a2,a3,a4,a6]
Generators	[-150:295:1]	Generators of the group modulo torsion
j	242702053576633/2554695936	j-invariant
L	2.715856329915	L(r)(E,1)/r!
Ω	0.30073283868781	Real period
R	0.90307940488479	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	30576br2 122304by2 11466bz2 95550hl2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3822m2

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	+	-2	8	0	6	4	-2	10	4	-8	-10	-4	2	-16	-8	-2	8	-12	-14	-10

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Quadratic twists for elliptic curve 3822m2

-4	8	-3	5	-7	13
30576br2	122304by2	11466bz2	95550hl2	78a2	49686dd2

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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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