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	17328p	Isogeny class
Conductor	17328	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-142228224 = -1 · 28 · 34 · 193	Discriminant
Eigenvalues	2- 3+ -1 -1 -1 -4 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-101,729]	[a1,a2,a3,a4,a6]
Generators	[5:18:1] [13:38:1]	Generators of the group modulo torsion
j	-65536/81	j-invariant
L	5.7628741760339	L(r)(E,1)/r!
Ω	1.6613500110033	Real period
R	0.43359874032157	Regulator
r	2	Rank of the group of rational points
S	0.99999999999996	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4332b1 69312cz1 51984cb1 17328bb1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 17328p1

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	-1	-1	-4	-3	+	-4	-8	-4	-4	-4	-1	-3	4	-4	-5	8	12	-11	0	-8	-12	12

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Quadratic twists for elliptic curve 17328p1

-4	8	-3	-19
4332b1	69312cz1	51984cb1	17328bb1

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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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