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	17472d	Isogeny class
Conductor	17472	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-2290089984 = -1 · 223 · 3 · 7 · 13	Discriminant
Eigenvalues	2+ 3+ -1 7+ -3 13-  5 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-481,-4511]	[a1,a2,a3,a4,a6]
j	-47045881/8736	j-invariant
L	1.0091013996946	L(r)(E,1)/r!
Ω	0.50455069984732	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17472db1 546b1 52416bx1 122304cz1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472d1

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
+	+	-1	+	-3	-	5	-1	3	-5	4	5	-8	1	8	-6	0	-13	10	8	-15	6	2	-2	-2

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Quadratic twists for elliptic curve 17472d1

-4	8	-3	-7
17472db1	546b1	52416bx1	122304cz1

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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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