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	16	Product of Tamagawa factors cp
Δ	-138683817657 = -1 · 37 · 78 · 11	Discriminant
Eigenvalues	1 3-  2 7- 11-  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,1134,-10535]	[a1,a2,a3,a4,a6]
j	221115865823/190238433	j-invariant
L	2.2826659690383	L(r)(E,1)/r!
Ω	0.57066649225957	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11088bh4 44352cf3 231a4 17325u4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 693d4

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 693d4

-4	8	-3	5	-7	-11	13
11088bh4	44352cf3	231a4	17325u4	4851o4	7623i4	117117r3

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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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