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	3822s	Isogeny class
Conductor	3822	Conductor
∏ cp	22	Product of Tamagawa factors cp
deg	24640	Modular degree for the optimal curve
Δ	-261072987162624 = -1 · 211 · 35 · 79 · 13	Discriminant
Eigenvalues	2- 3+  3 7- -5 13+ -3 -3	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-11369,-911401]	[a1,a2,a3,a4,a6]
Generators	[167:1288:1]	Generators of the group modulo torsion
j	-4027268071/6469632	j-invariant
L	5.0495315123291	L(r)(E,1)/r!
Ω	0.21894180451278	Real period
R	1.0483341002971	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	30576cq1 122304em1 11466t1 95550es1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3822s1

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

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Quadratic twists for elliptic curve 3822s1

-4	8	-3	5	-7	13
30576cq1	122304em1	11466t1	95550es1	3822bh1	49686p1

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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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