Cremona's table of elliptic curves

684 = 2² · 3² · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 19-	Signs for the Atkin-Lehner involutions
Class	684c	Isogeny class
Conductor	684	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-31912704 = -1 · 28 · 38 · 19	Discriminant
Eigenvalues	2- 3-  3  1  5 -6  5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,24,-268]	[a1,a2,a3,a4,a6]
j	8192/171	j-invariant
L	2.0213438944396	L(r)(E,1)/r!
Ω	1.0106719472198	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2736p1 10944v1 228b1 17100w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 684c1

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
-	-	3	1	5	-6	5	-	-4	-6	6	-8	8	9	-1	-2	8	11	0	4	-11	-8	4	-10	-10

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Quadratic twists for elliptic curve 684c1

-4	8	-3	5	-7	-11	13	-19
2736p1	10944v1	228b1	17100w1	33516p1	82764k1	115596r1	12996p1

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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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