Cremona's table of elliptic curves

693 = 3² · 7 · 11

Field	Data	Notes
Atkin-Lehner	3- 7- 11-	Signs for the Atkin-Lehner involutions
Class	693d	Isogeny class
Conductor	693	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	42362284041 = 310 · 72 · 114	Discriminant
Eigenvalues	1 3-  2 7- 11-  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2556,49387]	[a1,a2,a3,a4,a6]
j	2533811507137/58110129	j-invariant
L	2.2826659690383	L(r)(E,1)/r!
Ω	1.1413329845191	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	11088bh3 44352cf4 231a3 17325u3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 693d3

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	-	2	-	-	6	-2	4	0	2	8	6	-10	-4	8	-6	-4	-10	-12	0	2	16	-4	-18	2

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Quadratic twists for elliptic curve 693d3

-4	8	-3	5	-7	-11	13
11088bh3	44352cf4	231a3	17325u3	4851o3	7623i3	117117r4

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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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