Cremona's table of elliptic curves

17472 = 2⁶ · 3 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	17472cq	Isogeny class
Conductor	17472	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-9605333580251136 = -1 · 245 · 3 · 7 · 13	Discriminant
Eigenvalues	2- 3- -3 7+  3 13+ -3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1667617,828339551]	[a1,a2,a3,a4,a6]
Generators	[975557:786432:1331]	Generators of the group modulo torsion
j	-1956469094246217097/36641439744	j-invariant
L	4.4962732688753	L(r)(E,1)/r!
Ω	0.37622717940755	Real period
R	2.9877382037866	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	17472i3 4368p3 52416ev3 122304gj3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472cq3

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	+	-3	-7	-9	9	4	7	12	-1	0	6	12	1	14	-12	-7	10	-6	-6	-10

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Quadratic twists for elliptic curve 17472cq3

-4	8	-3	-7
17472i3	4368p3	52416ev3	122304gj3

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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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