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	27600dj	Isogeny class
Conductor	27600	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	2119680000 = 214 · 32 · 54 · 23	Discriminant
Eigenvalues	2- 3- 5-  5  3 -5 -6  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-408,-2412]	[a1,a2,a3,a4,a6]
Generators	[-12:30:1]	Generators of the group modulo torsion
j	2941225/828	j-invariant
L	8.0053792217251	L(r)(E,1)/r!
Ω	1.0847077581079	Real period
R	0.61501812829979	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3450f1 110400hl1 82800fl1 27600bp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600dj1

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	3	-5	-6	1	-	-5	8	-4	-7	-7	-6	-8	10	-12	-12	-10	-15	5	-9	14	-16

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Quadratic twists for elliptic curve 27600dj1

-4	8	-3	5
3450f1	110400hl1	82800fl1	27600bp1

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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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