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	3822r	Isogeny class
Conductor	3822	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	10752	Modular degree for the optimal curve
Δ	-7867154747088 = -1 · 24 · 38 · 78 · 13	Discriminant
Eigenvalues	2- 3+  0 7+ -5 13+  7  7	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-3823,-164347]	[a1,a2,a3,a4,a6]
j	-1071912625/1364688	j-invariant
L	2.3177976034825	L(r)(E,1)/r!
Ω	0.28972470043531	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	30576ci1 122304cl1 11466j1 95550dh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3822r1

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
-	+	0	+	-5	+	7	7	2	-9	0	4	4	2	-3	1	7	13	3	9	-10	14	16	-12	6

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Quadratic twists for elliptic curve 3822r1

-4	8	-3	5	-7	13
30576ci1	122304cl1	11466j1	95550dh1	3822bf1	49686b1

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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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