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	27600t	Isogeny class
Conductor	27600	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	574759346400000000 = 211 · 310 · 58 · 233	Discriminant
Eigenvalues	2+ 3- 5+  0 -2  0 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-12968008,-17978836012]	[a1,a2,a3,a4,a6]
j	7536914291382802562/17961229575	j-invariant
L	1.5911506194241	L(r)(E,1)/r!
Ω	0.079557530971184	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	13800d2 110400fj2 82800be2 5520d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600t2

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	0	-6	-8	+	-8	8	2	6	6	-4	6	0	2	-2	-14	-6	-16	0	16	4

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Quadratic twists for elliptic curve 27600t2

-4	8	-3	5
13800d2	110400fj2	82800be2	5520d2

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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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