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	17472bw	Isogeny class
Conductor	17472	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-15155833038667776 = -1 · 215 · 34 · 7 · 138	Discriminant
Eigenvalues	2- 3+ -2 7+  0 13- -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-13889,-5951871]	[a1,a2,a3,a4,a6]
Generators	[1265:44712:1]	Generators of the group modulo torsion
j	-9043113453704/462519318807	j-invariant
L	3.1605704666653	L(r)(E,1)/r!
Ω	0.17269203290826	Real period
R	4.5754433679408	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	17472dd4 8736v4 52416fh3 122304hf3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472bw4

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

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Quadratic twists for elliptic curve 17472bw4

-4	8	-3	-7
17472dd4	8736v4	52416fh3	122304hf3

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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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