Cremona's table of elliptic curves

684 = 2² · 3² · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 19+	Signs for the Atkin-Lehner involutions
Conductor	684	Conductor
Count	2	Number of curves in isogeny class
Curves	684b1 684b2	Curves in isogeny class
deg	144	Modular degree for the optimal curve
Eigenvalues	2- 3- -2  0 -2  2 -6 19+	Hecke eigenvalues for primes less than 20
L	2.0174937497296	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	2736u 10944bf 228a 17100m	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 684b

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	-2	2	-6	+	-2	-4	-8	-2	8	-8	-2	4	0	2	12	4	6	-16	-6	0	-2

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Quadratic twists for isogeny class 684b

-4	8	-3	5	-7	-11	13	-19
2736u	10944bf	228a	17100m	33516v	82764n	115596w	12996o

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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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