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	5175s	Isogeny class
Conductor	5175	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1527892875 = 312 · 53 · 23	Discriminant
Eigenvalues	-1 3- 5-  2  0  4 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-5495,158132]	[a1,a2,a3,a4,a6]
Generators	[39:25:1]	Generators of the group modulo torsion
j	201333092381/16767	j-invariant
L	2.6575448438645	L(r)(E,1)/r!
Ω	1.4386338175407	Real period
R	0.92363491371535	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	82800fs2 1725u2 5175w2 119025cn2	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 5175s2

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

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Quadratic twists for elliptic curve 5175s2

-4	-3	5	-23
82800fs2	1725u2	5175w2	119025cn2

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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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