Cremona's table of elliptic curves

3978 = 2 · 3² · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 13+ 17-	Signs for the Atkin-Lehner involutions
Class	3978d	Isogeny class
Conductor	3978	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-15091026041729664 = -1 · 27 · 322 · 13 · 172	Discriminant
Eigenvalues	2+ 3-  2 -4  2 13+ 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,58959,2123037]	[a1,a2,a3,a4,a6]
Generators	[7:1589:1]	Generators of the group modulo torsion
j	31091549545392623/20700995942016	j-invariant
L	2.7610638992799	L(r)(E,1)/r!
Ω	0.24723433641949	Real period
R	5.5839005602263	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	31824bf2 127296bv2 1326e2 99450dc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3978d2

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	+	-	0	2	0	-8	-2	8	-4	0	-2	4	8	-8	0	4	-6	-16	-14	4

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Quadratic twists for elliptic curve 3978d2

-4	8	-3	5	13	17
31824bf2	127296bv2	1326e2	99450dc2	51714v2	67626k2

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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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