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	80	Product of Tamagawa factors cp
Δ	85325073182595792 = 24 · 320 · 76 · 13	Discriminant
Eigenvalues	2+ 3- -2 7- -4 13+ -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-114637,5057336]	[a1,a2,a3,a4,a6]
Generators	[-233:4490:1]	Generators of the group modulo torsion
j	1416134368422073/725251155408	j-invariant
L	2.715856329915	L(r)(E,1)/r!
Ω	0.30073283868781	Real period
R	0.45153970244239	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30576br3 122304by3 11466bz3 95550hl3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3822m4

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 3822m4

-4	8	-3	5	-7	13
30576br3	122304by3	11466bz3	95550hl3	78a3	49686dd3

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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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