Cremona's table of elliptic curves

682 = 2 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2- 11+ 31-	Signs for the Atkin-Lehner involutions
Conductor	682	Conductor
Count	3	Number of curves in isogeny class
Curves	682a1 682a2 682a3	Curves in isogeny class
deg	72	Modular degree for the optimal curve
Eigenvalues	2- -2  0 -1 11+ -4 -3  2	Hecke eigenvalues for primes less than 20
L	2.2812508095831	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	5456h 21824m 6138i 17050b	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 682a

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	-1	+	-4	-3	2	-3	-6	-	-7	0	-1	-6	-6	3	8	5	12	2	-10	15	0	17

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Quadratic twists for isogeny class 682a

-4	8	-3	5	-7	-11	13	-31
5456h	21824m	6138i	17050b	33418be	7502c	115258f	21142d

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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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