Cremona's table of elliptic curves

747 = 3² · 83

Field	Data	Notes
Atkin-Lehner	3- 83-	Signs for the Atkin-Lehner involutions
Conductor	747	Conductor
Count	1	Number of curves in isogeny class
Curves	747e1	Curves in isogeny class
deg	64	Modular degree for the optimal curve
Eigenvalues	-1 3-  1 -4  3  2 -4 -1	Hecke eigenvalues for primes less than 20
L	1.5131984023175	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	11952l 47808k 249b 18675g	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 747e

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	-	1	-4	3	2	-4	-1	3	-4	-6	-9	2	4	-8	-7	9	-13	5	0	-12	-12	-	-9	-6

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Quadratic twists for isogeny class 747e

-4	8	-3	5	-7	-11	13	-83
11952l	47808k	249b	18675g	36603o	90387i	126243j	62001g

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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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