Cremona's table of elliptic curves

663 = 3 · 13 · 17

Field	Data	Notes
Atkin-Lehner	3+ 13- 17-	Signs for the Atkin-Lehner involutions
Class	663b	Isogeny class
Conductor	663	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	161726530797 = 316 · 13 · 172	Discriminant
Eigenvalues	-1 3+ -2  0  4 13- 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-20174,-1111138]	[a1,a2,a3,a4,a6]
Generators	[-658:427:8]	Generators of the group modulo torsion
j	908031902324522977/161726530797	j-invariant
L	1.1920969617698	L(r)(E,1)/r!
Ω	0.40059551251327	Real period
R	2.9758120711108	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10608ba5 42432s6 1989e5 16575f5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 663b5

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	0	4	-	-	-4	0	-2	-8	-2	2	-4	8	-10	4	14	-4	0	-14	-8	-4	-6	-6

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Quadratic twists for elliptic curve 663b5

-4	8	-3	5	-7	-11	13	17
10608ba5	42432s6	1989e5	16575f5	32487l6	80223c6	8619b5	11271h5

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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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