Cremona's table of elliptic curves

3738 = 2 · 3 · 7 · 89

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 89+	Signs for the Atkin-Lehner involutions
Class	3738d	Isogeny class
Conductor	3738	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	6986322 = 2 · 32 · 72 · 892	Discriminant
Eigenvalues	2- 3-  0 7-  4  6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-83,255]	[a1,a2,a3,a4,a6]
j	63282696625/6986322	j-invariant
L	4.5750574294689	L(r)(E,1)/r!
Ω	2.2875287147344	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	29904a2 119616c2 11214f2 93450b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3738d2

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	-	4	6	-6	4	0	-4	8	-8	-6	10	8	-10	0	-6	16	0	-6	-8	-4	+	-10

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Quadratic twists for elliptic curve 3738d2

-4	8	-3	5	-7
29904a2	119616c2	11214f2	93450b2	26166q2

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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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