Cremona's table of elliptic curves

115520 = 2⁶ · 5 · 19²

Field	Data	Notes
Atkin-Lehner	2- 5+ 19+	Signs for the Atkin-Lehner involutions
Class	115520bk	Isogeny class
Conductor	115520	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	143360	Modular degree for the optimal curve
Δ	-561889280000 = -1 · 217 · 54 · 193	Discriminant
Eigenvalues	2-  1 5+ -1  2  1 -5 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-6561,205535]	[a1,a2,a3,a4,a6]
Generators	[-89:304:1] [7:400:1]	Generators of the group modulo torsion
j	-34747958/625	j-invariant
L	12.798423309463	L(r)(E,1)/r!
Ω	0.92255071905239	Real period
R	0.86705418000391	Regulator
r	2	Rank of the group of rational points
S	0.99999999952679	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	115520d1 28880e1 115520bm1	Quadratic twists by: -4 8 -19

Hecke Eigenvalues for elliptic curve 115520bk1

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	+	-1	2	1	-5	+	-9	5	-10	-10	0	2	-8	-7	-3	12	13	4	-7	4	-6	-2	-12

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Quadratic twists for elliptic curve 115520bk1

-4	8	-19
115520d1	28880e1	115520bm1

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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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