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	117600cn	Isogeny class
Conductor	117600	Conductor
∏ cp	192	Product of Tamagawa factors cp
deg	1769472	Modular degree for the optimal curve
Δ	5148111413025000000 = 26 · 36 · 58 · 710	Discriminant
Eigenvalues	2+ 3- 5+ 7-  0  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1090658,424238688]	[a1,a2,a3,a4,a6]
Generators	[13:20250:1]	Generators of the group modulo torsion
j	1219555693504/43758225	j-invariant
L	8.188222909529	L(r)(E,1)/r!
Ω	0.24054411438831	Real period
R	2.8367017368226	Regulator
r	1	Rank of the group of rational points
S	1.0000000030184	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	117600ek1 23520bc1 16800g1	Quadratic twists by: -4 5 -7

Hecke Eigenvalues for elliptic curve 117600cn1

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	-2	-4	-8	-2	-4	6	6	4	0	-6	0	-6	-4	8	10	12	4	6	-6

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Quadratic twists for elliptic curve 117600cn1

-4	5	-7
117600ek1	23520bc1	16800g1

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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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