Cremona's table of elliptic curves

115600 = 2⁴ · 5² · 17²

Field	Data	Notes
Atkin-Lehner	2- 5- 17+	Signs for the Atkin-Lehner involutions
Class	115600dc	Isogeny class
Conductor	115600	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	293760	Modular degree for the optimal curve
Δ	-19394461696000 = -1 · 229 · 53 · 172	Discriminant
Eigenvalues	2- -2 5-  3  3 -3 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-10568,465268]	[a1,a2,a3,a4,a6]
Generators	[478:10240:1]	Generators of the group modulo torsion
j	-882216989/131072	j-invariant
L	5.671716936241	L(r)(E,1)/r!
Ω	0.66271508017981	Real period
R	1.069787957705	Regulator
r	1	Rank of the group of rational points
S	1.0000000068611	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	14450n1 115600db1 115600dg2	Quadratic twists by: -4 5 17

Hecke Eigenvalues for elliptic curve 115600dc1

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	-	3	3	-3	+	4	-5	8	8	-2	-6	10	-3	3	-11	-12	8	-12	2	14	-16	5	18

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Quadratic twists for elliptic curve 115600dc1

-4	5	17
14450n1	115600db1	115600dg2

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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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