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	3822bd	Isogeny class
Conductor	3822	Conductor
∏ cp	108	Product of Tamagawa factors cp
deg	60480	Modular degree for the optimal curve
Δ	660840998755392 = 26 · 39 · 79 · 13	Discriminant
Eigenvalues	2- 3- -2 7-  4 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1827554,-951092220]	[a1,a2,a3,a4,a6]
j	16728308209329751/16376256	j-invariant
L	3.5058698419969	L(r)(E,1)/r!
Ω	0.12984703118507	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30576bt1 122304ca1 11466o1 95550bo1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3822bd1

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

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Quadratic twists for elliptic curve 3822bd1

-4	8	-3	5	-7	13
30576bt1	122304ca1	11466o1	95550bo1	3822w1	49686bi1

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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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