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	27600w	Isogeny class
Conductor	27600	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	-37260000000 = -1 · 28 · 34 · 57 · 23	Discriminant
Eigenvalues	2+ 3- 5+  3  6  2 -3  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5033,-139437]	[a1,a2,a3,a4,a6]
j	-3525581824/9315	j-invariant
L	4.5337428739184	L(r)(E,1)/r!
Ω	0.28335892961989	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13800h1 110400fv1 82800bm1 5520b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600w1

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
+	-	+	3	6	2	-3	6	+	-9	3	-3	-3	0	4	9	3	-8	3	9	-6	4	3	-8	-18

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Quadratic twists for elliptic curve 27600w1

-4	8	-3	5
13800h1	110400fv1	82800bm1	5520b1

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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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