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	128	Product of Tamagawa factors cp
Δ	27423360000000000 = 216 · 34 · 510 · 232	Discriminant
Eigenvalues	2- 3- 5+  0 -4  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2760008,-1765776012]	[a1,a2,a3,a4,a6]
Generators	[4084:234726:1]	Generators of the group modulo torsion
j	36330796409313601/428490000	j-invariant
L	6.5675404709303	L(r)(E,1)/r!
Ω	0.11713111128112	Real period
R	7.0087489983428	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	3450d2 110400fl2 82800du2 5520u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600ch2

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 27600ch2

-4	8	-3	5
3450d2	110400fl2	82800du2	5520u2

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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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