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	3822h	Isogeny class
Conductor	3822	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	-1027781664 = -1 · 25 · 3 · 77 · 13	Discriminant
Eigenvalues	2+ 3+ -1 7-  3 13- -5 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-368,2976]	[a1,a2,a3,a4,a6]
Generators	[13:18:1]	Generators of the group modulo torsion
j	-47045881/8736	j-invariant
L	2.1572630740605	L(r)(E,1)/r!
Ω	1.4964096804518	Real period
R	0.36040649533373	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	30576cy1 122304cz1 11466cj1 95550jj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3822h1

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
+	+	-1	-	3	-	-5	-1	3	5	-4	-5	8	-1	-8	6	0	-13	-10	8	15	6	2	2	2

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Quadratic twists for elliptic curve 3822h1

-4	8	-3	5	-7	13
30576cy1	122304cz1	11466cj1	95550jj1	546b1	49686cb1

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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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