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
deg	144	Modular degree for the optimal curve
Δ	-30255687 = -1 · 36 · 73 · 112	Discriminant
Eigenvalues	-1 3-  2 7+ 11+  4 -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,31,-264]	[a1,a2,a3,a4,a6]
j	4657463/41503	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	11088by1 44352br1 77c1 17325x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 693a1

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 693a1

-4	8	-3	5	-7	-11	13
11088by1	44352br1	77c1	17325x1	4851k1	7623o1	117117br1

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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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