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	27600ck	Isogeny class
Conductor	27600	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	2939448773836800 = 230 · 32 · 52 · 233	Discriminant
Eigenvalues	2- 3- 5+ -1  3  1 -6  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-42688,2158388]	[a1,a2,a3,a4,a6]
Generators	[44:606:1]	Generators of the group modulo torsion
j	84013940106985/28705554432	j-invariant
L	6.6529593811447	L(r)(E,1)/r!
Ω	0.41516170824969	Real period
R	4.0062457886551	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	3450q2 110400fo2 82800dy2 27600cc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600ck2

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
-	-	+	-1	3	1	-6	1	+	-9	4	4	9	-1	6	-12	6	-4	-4	6	7	1	-15	-18	4

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Quadratic twists for elliptic curve 27600ck2

-4	8	-3	5
3450q2	110400fo2	82800dy2	27600cc2

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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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