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	40	Product of Tamagawa factors cp
Δ	13064352970032 = 24 · 35 · 76 · 134	Discriminant
Eigenvalues	2+ 3- -2 7- -4 13+ -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1016237,-394396936]	[a1,a2,a3,a4,a6]
Generators	[-582:295:1]	Generators of the group modulo torsion
j	986551739719628473/111045168	j-invariant
L	2.715856329915	L(r)(E,1)/r!
Ω	0.15036641934391	Real period
R	1.8061588097696	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	30576br4 122304by4 11466bz4 95550hl4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3822m3

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 3822m3

-4	8	-3	5	-7	13
30576br4	122304by4	11466bz4	95550hl4	78a4	49686dd4

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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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