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	5175v	Isogeny class
Conductor	5175	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-6778845703125 = -1 · 38 · 59 · 232	Discriminant
Eigenvalues	1 3- 5-  0  0 -4  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,4383,-57834]	[a1,a2,a3,a4,a6]
j	6539203/4761	j-invariant
L	1.6815651260025	L(r)(E,1)/r!
Ω	0.42039128150063	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	82800ey2 1725r2 5175r2 119025cc2	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 5175v2

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 5175v2

-4	-3	5	-23
82800ey2	1725r2	5175r2	119025cc2

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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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