Cremona's table of elliptic curves

119616 = 2⁶ · 3 · 7 · 89

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 89-	Signs for the Atkin-Lehner involutions
Class	119616s	Isogeny class
Conductor	119616	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	6309822468096 = 212 · 34 · 74 · 892	Discriminant
Eigenvalues	2- 3+  2 7+  0 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-11737,-470375]	[a1,a2,a3,a4,a6]
Generators	[48475:281520:343]	Generators of the group modulo torsion
j	43658828648128/1540484001	j-invariant
L	6.4972561794098	L(r)(E,1)/r!
Ω	0.45967182305444	Real period
R	7.0672769689185	Regulator
r	1	Rank of the group of rational points
S	1.0000000004222	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	119616ba2 59808j1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 119616s2

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	+	0	-2	2	4	0	-2	-8	6	2	4	-8	-6	12	-2	8	16	10	0	4	-	2

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Quadratic twists for elliptic curve 119616s2

-4	8
119616ba2	59808j1

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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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