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	17328o	Isogeny class
Conductor	17328	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	69120	Modular degree for the optimal curve
Δ	-166817919419136 = -1 · 28 · 36 · 197	Discriminant
Eigenvalues	2+ 3- -3  3  1  2 -5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-20697,1296819]	[a1,a2,a3,a4,a6]
Generators	[6:1083:1]	Generators of the group modulo torsion
j	-81415168/13851	j-invariant
L	5.6236260854223	L(r)(E,1)/r!
Ω	0.5519399192447	Real period
R	0.42453489118872	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	8664k1 69312cv1 51984z1 912a1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 17328o1

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
+	-	-3	3	1	2	-5	-	4	6	-2	-8	8	-13	-13	6	4	-13	4	-8	-3	-4	-4	6	-2

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Quadratic twists for elliptic curve 17328o1

-4	8	-3	-19
8664k1	69312cv1	51984z1	912a1

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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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