Cremona's table of elliptic curves

39675 = 3 · 5² · 23²

Field	Data	Notes
Atkin-Lehner	3- 5+ 23-	Signs for the Atkin-Lehner involutions
Class	39675bc	Isogeny class
Conductor	39675	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	379399792081640625 = 38 · 58 · 236	Discriminant
Eigenvalues	1 3- 5+  0  4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1785651,917796073]	[a1,a2,a3,a4,a6]
Generators	[5806:13593:8]	Generators of the group modulo torsion
j	272223782641/164025	j-invariant
L	9.0214388233273	L(r)(E,1)/r!
Ω	0.29770070945082	Real period
R	3.7879649497517	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	119025be6 7935b5 75b5	Quadratic twists by: -3 5 -23

Hecke Eigenvalues for elliptic curve 39675bc6

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	-	+	0	4	2	2	-4	-	-2	0	-10	10	4	-8	-10	-4	2	12	-8	-10	0	12	6	2

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Quadratic twists for elliptic curve 39675bc6

-3	5	-23
119025be6	7935b5	75b5

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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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