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	117600fq	Isogeny class
Conductor	117600	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	209664	Modular degree for the optimal curve
Δ	-691776120000 = -1 · 26 · 3 · 54 · 78	Discriminant
Eigenvalues	2- 3+ 5- 7+ -6 -1  6 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2858,-70188]	[a1,a2,a3,a4,a6]
Generators	[82:490:1]	Generators of the group modulo torsion
j	-11200/3	j-invariant
L	4.1779744164843	L(r)(E,1)/r!
Ω	0.32196758153494	Real period
R	0.72091012804688	Regulator
r	1	Rank of the group of rational points
S	0.99999999730034	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	117600hn1 117600cj1 117600if1	Quadratic twists by: -4 5 -7

Hecke Eigenvalues for elliptic curve 117600fq1

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
-	+	-	+	-6	-1	6	-5	-8	-2	-4	1	6	12	12	6	-8	-15	5	6	1	1	4	-4	13

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Quadratic twists for elliptic curve 117600fq1

-4	5	-7
117600hn1	117600cj1	117600if1

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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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