Cremona's table of elliptic curves

129960 = 2³ · 3² · 5 · 19²

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 19-	Signs for the Atkin-Lehner involutions
Class	129960r	Isogeny class
Conductor	129960	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2502268791287040000 = 211 · 37 · 54 · 197	Discriminant
Eigenvalues	2+ 3- 5+  0 -4 -2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7928643,8592694558]	[a1,a2,a3,a4,a6]
Generators	[6258:451724:1]	Generators of the group modulo torsion
j	784767874322/35625	j-invariant
L	4.1798975417464	L(r)(E,1)/r!
Ω	0.2421077518727	Real period
R	8.6323082739366	Regulator
r	1	Rank of the group of rational points
S	1.000000010143	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	43320bg4 6840m3	Quadratic twists by: -3 -19

Hecke Eigenvalues for elliptic curve 129960r4

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	-2	-6	-	4	-10	-4	-10	6	0	12	10	0	-10	-4	0	10	-4	-12	14	2

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Quadratic twists for elliptic curve 129960r4

-3	-19
43320bg4	6840m3

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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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