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	27600cf	Isogeny class
Conductor	27600	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	614400	Modular degree for the optimal curve
Δ	1584119332800000000 = 212 · 316 · 58 · 23	Discriminant
Eigenvalues	2- 3+ 5-  5 -5  1  0  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-332208,-41897088]	[a1,a2,a3,a4,a6]
j	2534167381585/990074583	j-invariant
L	2.4672086995921	L(r)(E,1)/r!
Ω	0.20560072496593	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	1725s1 110400jt1 82800fm1 27600ct1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600cf1

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
-	+	-	5	-5	1	0	7	-	3	-2	0	3	11	-10	-10	4	-4	16	6	-3	1	15	-6	-14

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Quadratic twists for elliptic curve 27600cf1

-4	8	-3	5
1725s1	110400jt1	82800fm1	27600ct1

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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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