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	693a	Isogeny class
Conductor	693	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	943427331 = 36 · 76 · 11	Discriminant
Eigenvalues	-1 3-  2 7+ 11+  4 -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-464,-3432]	[a1,a2,a3,a4,a6]
j	15124197817/1294139	j-invariant
L	1.0344382277142	L(r)(E,1)/r!
Ω	1.0344382277142	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	11088by2 44352br2 77c2 17325x2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 693a2

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	+	+	4	-4	0	4	6	10	-6	-4	12	10	6	-2	0	8	12	-8	8	0	6	-10

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Quadratic twists for elliptic curve 693a2

-4	8	-3	5	-7	-11	13
11088by2	44352br2	77c2	17325x2	4851k2	7623o2	117117br2

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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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