Cremona's table of elliptic curves

111573 = 3² · 7² · 11 · 23

Field	Data	Notes
Atkin-Lehner	3- 7- 11+ 23+	Signs for the Atkin-Lehner involutions
Class	111573y	Isogeny class
Conductor	111573	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	769707427797 = 36 · 73 · 11 · 234	Discriminant
Eigenvalues	-1 3- -4 7- 11+  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3002,-46420]	[a1,a2,a3,a4,a6]
Generators	[-33:142:1]	Generators of the group modulo torsion
j	11961853903/3078251	j-invariant
L	2.417401229201	L(r)(E,1)/r!
Ω	0.65726310113353	Real period
R	1.8389905722246	Regulator
r	1	Rank of the group of rational points
S	0.99999997364511	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12397n2 111573x2	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 111573y2

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	-	-4	-	+	2	-6	4	+	-2	10	6	2	-8	-6	6	-14	-10	-4	8	-14	4	12	12	8

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Quadratic twists for elliptic curve 111573y2

-3	-7
12397n2	111573x2

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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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