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	17472bn	Isogeny class
Conductor	17472	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	7096320	Modular degree for the optimal curve
Δ	-2.2378269592825E+23	Discriminant
Eigenvalues	2+ 3-  3 7- -6 13- -8  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-443517989,3595057300803]	[a1,a2,a3,a4,a6]
j	-588894491652244161881463808/13658611812026920011	j-invariant
L	3.3135836237523	L(r)(E,1)/r!
Ω	0.092043989548675	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	17472bz1 2184d1 52416dm1 122304bm1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472bn1

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
+	-	3	-	-6	-	-8	1	1	5	3	-12	10	11	-3	1	8	-2	-2	8	11	13	7	7	-1

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Quadratic twists for elliptic curve 17472bn1

-4	8	-3	-7
17472bz1	2184d1	52416dm1	122304bm1

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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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