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	27600j	Isogeny class
Conductor	27600	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	149040000000 = 210 · 34 · 57 · 23	Discriminant
Eigenvalues	2+ 3+ 5+  4 -4 -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-61408,-5836688]	[a1,a2,a3,a4,a6]
j	1600610497636/9315	j-invariant
L	1.2131175063803	L(r)(E,1)/r!
Ω	0.303279376595	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	13800w3 110400iq4 82800z4 5520e3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600j4

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
+	+	+	4	-4	-6	2	-4	-	-2	0	-2	2	0	0	6	8	-2	-16	4	-10	0	4	6	2

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Quadratic twists for elliptic curve 27600j4

-4	8	-3	5
13800w3	110400iq4	82800z4	5520e3

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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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