Cremona's table of elliptic curves

117600 = 2⁵ · 3 · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	117600cp	Isogeny class
Conductor	117600	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	508455448200000000 = 29 · 32 · 58 · 710	Discriminant
Eigenvalues	2+ 3- 5+ 7-  0  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2960008,1958854988]	[a1,a2,a3,a4,a6]
Generators	[17903:2384850:1]	Generators of the group modulo torsion
j	3047363673992/540225	j-invariant
L	8.6797775489983	L(r)(E,1)/r!
Ω	0.28477618926895	Real period
R	7.6198237342935	Regulator
r	1	Rank of the group of rational points
S	1.0000000098142	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	117600m4 23520bj4 16800h2	Quadratic twists by: -4 5 -7

Hecke Eigenvalues for elliptic curve 117600cp4

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	2	-6	4	-8	-2	8	2	6	0	0	-6	4	6	8	0	-14	8	-4	-2	-14

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Quadratic twists for elliptic curve 117600cp4

-4	5	-7
117600m4	23520bj4	16800h2

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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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