Cremona's table of elliptic curves

5175 = 3² · 5² · 23

Field	Data	Notes
Atkin-Lehner	3- 5+ 23+	Signs for the Atkin-Lehner involutions
Class	5175c	Isogeny class
Conductor	5175	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	5559500832275390625 = 316 · 512 · 232	Discriminant
Eigenvalues	1 3- 5+ -4 -4 -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-492417,-69299384]	[a1,a2,a3,a4,a6]
j	1159246431432649/488076890625	j-invariant
L	0.37425119890875	L(r)(E,1)/r!
Ω	0.18712559945437	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	82800eq2 1725g2 1035g2 119025bc2	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 5175c2

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	-	+	-4	-4	-6	-2	-4	+	10	-8	-2	-2	8	0	-6	0	6	-8	4	-10	16	-12	10	10

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Quadratic twists for elliptic curve 5175c2

-4	-3	5	-23
82800eq2	1725g2	1035g2	119025bc2

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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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