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	5175r	Isogeny class
Conductor	5175	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-433846125 = -1 · 38 · 53 · 232	Discriminant
Eigenvalues	-1 3- 5-  0  0  4  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,175,-498]	[a1,a2,a3,a4,a6]
Generators	[14:60:1]	Generators of the group modulo torsion
j	6539203/4761	j-invariant
L	2.486478909968	L(r)(E,1)/r!
Ω	0.94002348258366	Real period
R	0.66128106266396	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	82800fn2 1725k2 5175v2 119025cm2	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 5175r2

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	-	-	0	0	4	0	-2	+	2	-8	-10	2	-4	0	0	14	6	-4	6	8	-6	0	6	-6

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Quadratic twists for elliptic curve 5175r2

-4	-3	5	-23
82800fn2	1725k2	5175v2	119025cm2

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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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