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	693c	Isogeny class
Conductor	693	Conductor
∏ cp	18	Product of Tamagawa factors cp
Δ	-114154707051 = -1 · 36 · 76 · 113	Discriminant
Eigenvalues	0 3- -3 7- 11- -4  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-444,-16650]	[a1,a2,a3,a4,a6]
j	-13278380032/156590819	j-invariant
L	0.8965723977233	L(r)(E,1)/r!
Ω	0.44828619886165	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	11088bj2 44352ch2 77b1 17325n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 693c2

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
0	-	-3	-	-	-4	6	2	-3	6	5	11	-6	8	0	6	9	-10	5	-9	2	-10	-12	3	-1

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Quadratic twists for elliptic curve 693c2

-4	8	-3	5	-7	-11	13
11088bj2	44352ch2	77b1	17325n2	4851n2	7623f2	117117n2

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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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