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	2	Number of curves in isogeny class
Curves	747b1 747b2	Curves in isogeny class
deg	28	Modular degree for the optimal curve
Eigenvalues	1 3+  2  0  0  6  4  2	Hecke eigenvalues for primes less than 20
L	2.2522275159788	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	11952h 47808b 747a 18675b	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 747b

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	+	2	0	0	6	4	2	4	4	-4	-2	8	-2	0	-6	4	2	-14	-8	6	2	-	6	-2

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Quadratic twists for isogeny class 747b

-4	8	-3	5	-7	-11	13	-83
11952h	47808b	747a	18675b	36603a	90387b	126243a	62001d

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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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