Cremona's table of elliptic curves

27744 = 2⁵ · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3+ 17+	Signs for the Atkin-Lehner involutions
Class	27744r	Isogeny class
Conductor	27744	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	36162326574144 = 26 · 34 · 178	Discriminant
Eigenvalues	2- 3+ -2  0 -4 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-29574,1945944]	[a1,a2,a3,a4,a6]
Generators	[-181:1156:1] [27:1080:1]	Generators of the group modulo torsion
j	1851804352/23409	j-invariant
L	6.2208184038909	L(r)(E,1)/r!
Ω	0.65344801738275	Real period
R	9.5199897136533	Regulator
r	2	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	27744z1 55488dp2 83232i1 1632l1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 27744r1

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

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Quadratic twists for elliptic curve 27744r1

-4	8	-3	17
27744z1	55488dp2	83232i1	1632l1

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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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