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	16	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	-1301538375 = -1 · 39 · 53 · 232	Discriminant
Eigenvalues	-1 3- 5-  2  0  4 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-320,2882]	[a1,a2,a3,a4,a6]
Generators	[-6:70:1]	Generators of the group modulo torsion
j	-39651821/14283	j-invariant
L	2.6575448438645	L(r)(E,1)/r!
Ω	1.4386338175407	Real period
R	0.46181745685767	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	82800fs1 1725u1 5175w1 119025cn1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 5175s1

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 5175s1

-4	-3	5	-23
82800fs1	1725u1	5175w1	119025cn1

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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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