Cremona's table of elliptic curves

17696 = 2⁵ · 7 · 79

Field	Data	Notes
Atkin-Lehner	2- 7- 79+	Signs for the Atkin-Lehner involutions
Class	17696f	Isogeny class
Conductor	17696	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	1981952 = 29 · 72 · 79	Discriminant
Eigenvalues	2-  2 -4 7- -4 -4  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-840,9656]	[a1,a2,a3,a4,a6]
Generators	[507:332:27]	Generators of the group modulo torsion
j	128176534088/3871	j-invariant
L	4.9534031516956	L(r)(E,1)/r!
Ω	2.4436538972161	Real period
R	4.054095514376	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	17696a2 35392k2 123872j2	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 17696f2

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
-	2	-4	-	-4	-4	4	-4	8	6	-6	6	12	0	-12	-6	10	10	12	0	14	+	0	6	10

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Quadratic twists for elliptic curve 17696f2

-4	8	-7
17696a2	35392k2	123872j2

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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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