Cremona's table of elliptic curves

27600 = 2⁴ · 3 · 5² · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 23+	Signs for the Atkin-Lehner involutions
Class	27600ch	Isogeny class
Conductor	27600	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1324800000000 = 214 · 32 · 58 · 23	Discriminant
Eigenvalues	2- 3- 5+  0 -4  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-44160008,-112966176012]	[a1,a2,a3,a4,a6]
Generators	[54232156:-1231434366:6859]	Generators of the group modulo torsion
j	148809678420065817601/20700	j-invariant
L	6.5675404709303	L(r)(E,1)/r!
Ω	0.058565555640558	Real period
R	14.017497996686	Regulator
r	1	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3450d4 110400fl4 82800du4 5520u3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600ch4

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

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Quadratic twists for elliptic curve 27600ch4

-4	8	-3	5
3450d4	110400fl4	82800du4	5520u3

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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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