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	27744v	Isogeny class
Conductor	27744	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	-144324288 = -1 · 26 · 33 · 174	Discriminant
Eigenvalues	2- 3+ -2  5  2 -1 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-674,-6540]	[a1,a2,a3,a4,a6]
Generators	[40:170:1]	Generators of the group modulo torsion
j	-6344128/27	j-invariant
L	4.9621501118833	L(r)(E,1)/r!
Ω	0.46831740715446	Real period
R	1.7659497725534	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	27744bd1 55488eg1 83232v1 27744y1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 27744v1

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	5	2	-1	-	-1	4	-2	-1	-11	-2	5	6	0	4	-7	-5	10	6	0	-4	-12	-11

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Quadratic twists for elliptic curve 27744v1

-4	8	-3	17
27744bd1	55488eg1	83232v1	27744y1

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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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