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	17472bz	Isogeny class
Conductor	17472	Conductor
∏ cp	2	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]
Generators	[1290753325833369291281515673061667756464502022667931738197810914301106091947580386056639785355786067771107652492:692759592047298661159536394268939806531553193680461970258802920704250573612747874798991140991355151934887682331871:4456524501194500714747225738035068164575284699302584966320311746803472661129003935842121974070341277579353]	Generators of the group modulo torsion
j	-588894491652244161881463808/13658611812026920011	j-invariant
L	5.425137002419	L(r)(E,1)/r!
Ω	0.016449062271172	Real period
R	164.90718172813	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17472bn1 4368h1 52416fq1 122304hs1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472bz1

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 17472bz1

-4	8	-3	-7
17472bn1	4368h1	52416fq1	122304hs1

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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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