Cremona's table of elliptic curves

3838 = 2 · 19 · 101

Field	Data	Notes
Atkin-Lehner	2- 19+ 101+	Signs for the Atkin-Lehner involutions
Class	3838a	Isogeny class
Conductor	3838	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-559749272 = -1 · 23 · 193 · 1012	Discriminant
Eigenvalues	2-  1  2  1 -2  7  3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,68,-1112]	[a1,a2,a3,a4,a6]
j	34741712447/559749272	j-invariant
L	4.8009417000322	L(r)(E,1)/r!
Ω	0.80015695000537	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	30704d1 122816b1 34542a1 95950a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3838a1

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
-	1	2	1	-2	7	3	+	7	5	0	-2	-10	-2	4	-11	1	10	5	-8	11	0	8	8	-4

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Quadratic twists for elliptic curve 3838a1

-4	8	-3	5	-19
30704d1	122816b1	34542a1	95950a1	72922b1

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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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