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	17472dd	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	[-38:2535:1]	Generators of the group modulo torsion
j	-9043113453704/462519318807	j-invariant
L	5.2741142869728	L(r)(E,1)/r!
Ω	0.32627249860615	Real period
R	1.0102970503	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	17472bw4 8736s4 52416gm3 122304ff3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472dd4

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 17472dd4

-4	8	-3	-7
17472bw4	8736s4	52416gm3	122304ff3

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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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