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	3822o	Isogeny class
Conductor	3822	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	-289371264 = -1 · 27 · 3 · 73 · 133	Discriminant
Eigenvalues	2+ 3- -1 7-  5 13-  3  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-3099,-66650]	[a1,a2,a3,a4,a6]
j	-9591639636223/843648	j-invariant
L	1.9196847393309	L(r)(E,1)/r!
Ω	0.31994745655515	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	30576cb1 122304q1 11466ck1 95550gy1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3822o1

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	-	5	-	3	5	9	-1	-2	3	-12	7	-4	-10	14	-11	4	-10	-11	4	6	16	-14

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Quadratic twists for elliptic curve 3822o1

-4	8	-3	5	-7	13
30576cb1	122304q1	11466ck1	95550gy1	3822c1	49686cy1

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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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