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	27744r1 27744r2 27744r3 27744r4	Curves in isogeny class
deg	73728	Modular degree for the optimal curve
Eigenvalues	2- 3+ -2  0 -4 -2 17+  0	Hecke eigenvalues for primes less than 20
L	6.2208184038909	L(r)(E,1)/r!
r	2	Rank of the group of rational points
Twists	27744z 55488dp 83232i 1632l	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for isogeny class 27744r

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 isogeny class 27744r

-4	8	-3	17
27744z	55488dp	83232i	1632l

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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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