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	17472bh	Isogeny class
Conductor	17472	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	288414952390656 = 216 · 312 · 72 · 132	Discriminant
Eigenvalues	2+ 3-  2 7-  4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-707617,-229345345]	[a1,a2,a3,a4,a6]
Generators	[1538:48195:1]	Generators of the group modulo torsion
j	597914615076708388/4400862921	j-invariant
L	7.3288146113922	L(r)(E,1)/r!
Ω	0.16460769397484	Real period
R	3.7102430402961	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	17472br4 2184j3 52416cp4 122304cc4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472bh3

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	+	-6	-4	0	-6	0	-6	-6	-4	0	2	-4	2	-4	0	-6	8	-12	10	-14

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Quadratic twists for elliptic curve 17472bh3

-4	8	-3	-7
17472br4	2184j3	52416cp4	122304cc4

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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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