Cremona's table of elliptic curves

27900 = 2² · 3² · 5² · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 31-	Signs for the Atkin-Lehner involutions
Class	27900s	Isogeny class
Conductor	27900	Conductor
∏ cp	54	Product of Tamagawa factors cp
Δ	-10424466720000 = -1 · 28 · 37 · 54 · 313	Discriminant
Eigenvalues	2- 3- 5- -4  0 -4 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-26175,1637350]	[a1,a2,a3,a4,a6]
Generators	[95:90:1]	Generators of the group modulo torsion
j	-17003419600/89373	j-invariant
L	3.9049104591951	L(r)(E,1)/r!
Ω	0.72618156691493	Real period
R	0.89621995313205	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	111600gc2 9300m2 27900n2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 27900s2

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
-	-	-	-4	0	-4	-3	2	-6	3	-	2	6	5	-3	-6	12	-10	8	15	14	-1	12	-9	-13

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Quadratic twists for elliptic curve 27900s2

-4	-3	5
111600gc2	9300m2	27900n2

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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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