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	17472n	Isogeny class
Conductor	17472	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-19653623808 = -1 · 215 · 3 · 7 · 134	Discriminant
Eigenvalues	2+ 3+ -2 7-  4 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,671,673]	[a1,a2,a3,a4,a6]
Generators	[3:52:1]	Generators of the group modulo torsion
j	1018108216/599781	j-invariant
L	3.8986507617461	L(r)(E,1)/r!
Ω	0.74057687311485	Real period
R	2.6321715565789	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17472bb4 8736j4 52416db3 122304dg3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472n4

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
+	+	-2	-	4	-	-2	0	-8	2	8	6	6	4	-12	-6	4	-2	-12	-8	-2	-4	12	-10	6

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Quadratic twists for elliptic curve 17472n4

-4	8	-3	-7
17472bb4	8736j4	52416db3	122304dg3

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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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