Cremona's table of elliptic curves

51984 = 2⁴ · 3² · 19²

Field	Data	Notes
Atkin-Lehner	2- 3+ 19-	Signs for the Atkin-Lehner involutions
Class	51984bo	Isogeny class
Conductor	51984	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-14816065211568 = -1 · 24 · 39 · 196	Discriminant
Eigenvalues	2- 3+  0  4  0 -2  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,0,-185193]	[a1,a2,a3,a4,a6]
Generators	[52814205:1270868732:91125]	Generators of the group modulo torsion
j	0	j-invariant
L	7.1359219968014	L(r)(E,1)/r!
Ω	0.32168263671341	Real period
R	11.091556059297	Regulator
r	1	Rank of the group of rational points
S	0.99999999999757	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12996f3 51984bo1 144a3	Quadratic twists by: -4 -3 -19

Hecke Eigenvalues for elliptic curve 51984bo3

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	0	-2	0	-	0	0	-4	10	0	-8	0	0	0	14	-16	0	-10	-4	0	0	-14

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Quadratic twists for elliptic curve 51984bo3

-4	-3	-19
12996f3	51984bo1	144a3

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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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