Cremona's table of elliptic curves

27744 = 2⁵ · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 17+	Signs for the Atkin-Lehner involutions
Conductor	27744	Conductor
Count	4	Number of curves in isogeny class
Curves	27744f1 27744f2 27744f3 27744f4	Curves in isogeny class
deg	18432	Modular degree for the optimal curve
Eigenvalues	2+ 3+ -2  4 -4 -2 17+ -4	Hecke eigenvalues for primes less than 20
L	3.8183502536096	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	27744bb 55488bj 83232bn 96a	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for isogeny class 27744f

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	4	-4	-2	+	-4	0	-2	-4	2	-2	4	8	10	-4	-6	4	16	6	-4	12	10	14

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Quadratic twists for isogeny class 27744f

-4	8	-3	17
27744bb	55488bj	83232bn	96a

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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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