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	17328h	Isogeny class
Conductor	17328	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	57600	Modular degree for the optimal curve
Δ	2745973982208 = 210 · 3 · 197	Discriminant
Eigenvalues	2+ 3+  4 -4  4  4  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5896,156928]	[a1,a2,a3,a4,a6]
j	470596/57	j-invariant
L	3.118631191464	L(r)(E,1)/r!
Ω	0.77965779786601	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8664o1 69312dv1 51984bc1 912d1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 17328h1

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
+	+	4	-4	4	4	6	-	6	-2	2	-4	6	-4	2	6	-4	-10	8	0	-2	14	16	18	-14

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Quadratic twists for elliptic curve 17328h1

-4	8	-3	-19
8664o1	69312dv1	51984bc1	912d1

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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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