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	27600cr	Isogeny class
Conductor	27600	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	48384	Modular degree for the optimal curve
Δ	2425781250000 = 24 · 33 · 512 · 23	Discriminant
Eigenvalues	2- 3- 5+ -4  0 -2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4133,68238]	[a1,a2,a3,a4,a6]
Generators	[-62:300:1]	Generators of the group modulo torsion
j	31238127616/9703125	j-invariant
L	5.1477307591266	L(r)(E,1)/r!
Ω	0.75506023051067	Real period
R	2.2725475183373	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6900e1 110400gc1 82800es1 5520v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600cr1

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	0	-2	-6	-2	+	6	4	-8	6	8	12	6	6	-10	8	6	-2	10	-12	6	-8

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Quadratic twists for elliptic curve 27600cr1

-4	8	-3	5
6900e1	110400gc1	82800es1	5520v1

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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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