Cremona's table of elliptic curves

688 = 2⁴ · 43

Field	Data	Notes
Atkin-Lehner	2- 43+	Signs for the Atkin-Lehner involutions
Conductor	688	Conductor
Count	2	Number of curves in isogeny class
Curves	688b1 688b2	Curves in isogeny class
deg	48	Modular degree for the optimal curve
Eigenvalues	2-  2  0  4  3 -1 -3 -2	Hecke eigenvalues for primes less than 20
L	2.4922903027455	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	172a 2752f 6192n 17200y	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 688b

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	3	-1	-3	-2	3	6	-5	8	-3	+	12	-9	12	-10	-11	-6	-10	-8	15	0	-1

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Quadratic twists for isogeny class 688b

-4	8	-3	5	-7	-11	13	-43
172a	2752f	6192n	17200y	33712m	83248bn	116272n	29584m

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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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