Cremona's table of elliptic curves

17328 = 2⁴ · 3 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3- 19+	Signs for the Atkin-Lehner involutions
Class	17328ba	Isogeny class
Conductor	17328	Conductor
∏ cp	84	Product of Tamagawa factors cp
Δ	-152137942510252032 = -1 · 212 · 37 · 198	Discriminant
Eigenvalues	2- 3-  0 -1  2  5 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3829608,2883345012]	[a1,a2,a3,a4,a6]
Generators	[2286:77976:1]	Generators of the group modulo torsion
j	-89289015625/2187	j-invariant
L	6.2562738000996	L(r)(E,1)/r!
Ω	0.30101311962194	Real period
R	0.24742924858135	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1083a2 69312cc2 51984bx2 17328s2	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 17328ba2

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
-	-	0	-1	2	5	-4	+	4	-8	3	3	-12	1	6	4	-10	-13	-11	-6	-11	-1	0	-6	2

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Quadratic twists for elliptic curve 17328ba2

-4	8	-3	-19
1083a2	69312cc2	51984bx2	17328s2

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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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