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	117600l	Isogeny class
Conductor	117600	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	20338217928000000 = 29 · 32 · 56 · 710	Discriminant
Eigenvalues	2+ 3+ 5+ 7-  0  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-137608,18456712]	[a1,a2,a3,a4,a6]
j	306182024/21609	j-invariant
L	1.5064062027009	L(r)(E,1)/r!
Ω	0.37660171872494	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	117600cm3 4704be3 16800u2	Quadratic twists by: -4 5 -7

Hecke Eigenvalues for elliptic curve 117600l3

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	0	6	0	-6	6	-8	8	-6	12	-10	-16	-8	-6	8	-12	14	-6

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Quadratic twists for elliptic curve 117600l3

-4	5	-7
117600cm3	4704be3	16800u2

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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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