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	27600bz	Isogeny class
Conductor	27600	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	539136	Modular degree for the optimal curve
Δ	-5022323803422720000 = -1 · 225 · 39 · 54 · 233	Discriminant
Eigenvalues	2- 3+ 5- -5  0  2  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,369192,64457712]	[a1,a2,a3,a4,a6]
Generators	[-148:2560:1]	Generators of the group modulo torsion
j	2173899265153175/1961845235712	j-invariant
L	3.4228012803105	L(r)(E,1)/r!
Ω	0.15842170309339	Real period
R	1.8004694713939	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	3450m1 110400je1 82800fx1 27600dc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600bz1

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	0	2	3	-2	+	3	-2	-7	0	-2	3	-12	-6	2	-2	15	11	-8	9	3	-10

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Quadratic twists for elliptic curve 27600bz1

-4	8	-3	5
3450m1	110400je1	82800fx1	27600dc1

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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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