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	5175w	Isogeny class
Conductor	5175	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	23873326171875 = 312 · 59 · 23	Discriminant
Eigenvalues	1 3- 5- -2  0 -4  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-137367,19629166]	[a1,a2,a3,a4,a6]
j	201333092381/16767	j-invariant
L	1.2867532043005	L(r)(E,1)/r!
Ω	0.64337660215023	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	82800fg2 1725i2 5175s2 119025cg2	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 5175w2

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 5175w2

-4	-3	5	-23
82800fg2	1725i2	5175s2	119025cg2

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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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