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	1	Number of curves in isogeny class
Curves	684a1	Curves in isogeny class
deg	144	Modular degree for the optimal curve
Eigenvalues	2- 3-  1 -3 -5 -4  3 19+	Hecke eigenvalues for primes less than 20
L	2.1232510163787	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	2736r 10944bd 76a 17100r	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 684a

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	-3	-5	-4	3	+	-8	2	4	10	-10	1	1	4	-6	-13	-12	-2	9	8	12	-12	-8

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Quadratic twists for isogeny class 684a

-4	8	-3	5	-7	-11	13	-19
2736r	10944bd	76a	17100r	33516u	82764m	115596v	12996n

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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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