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	117600de	Isogeny class
Conductor	117600	Conductor
∏ cp	448	Product of Tamagawa factors cp
Δ	7.5360089154944E+29	Discriminant
Eigenvalues	2+ 3- 5+ 7-  4 -6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7840766033,263943665448063]	[a1,a2,a3,a4,a6]
Generators	[-40871:22718556:1]	Generators of the group modulo torsion
j	7079962908642659949376/100085966990454375	j-invariant
L	8.7297081252684	L(r)(E,1)/r!
Ω	0.028511205287758	Real period
R	2.7337961331975	Regulator
r	1	Rank of the group of rational points
S	0.99999999715907	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	117600bc3 23520bf3 16800i3	Quadratic twists by: -4 5 -7

Hecke Eigenvalues for elliptic curve 117600de3

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
+	-	+	-	4	-6	6	-4	-4	-2	8	-6	-6	8	0	-6	-4	-10	8	-12	-14	16	12	-14	18

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Quadratic twists for elliptic curve 117600de3

-4	5	-7
117600bc3	23520bf3	16800i3

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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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