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	17328bb	Isogeny class
Conductor	17328	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	72960	Modular degree for the optimal curve
Δ	-6691252101145344 = -1 · 28 · 34 · 199	Discriminant
Eigenvalues	2- 3- -1 -1 -1  4 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-36581,-4780977]	[a1,a2,a3,a4,a6]
Generators	[1203:41154:1]	Generators of the group modulo torsion
j	-65536/81	j-invariant
L	5.4905415609807	L(r)(E,1)/r!
Ω	0.16488174469629	Real period
R	2.0812422151002	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	4332a1 69312cd1 51984ca1 17328p1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 17328bb1

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 17328bb1

-4	8	-3	-19
4332a1	69312cd1	51984ca1	17328p1

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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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