Cremona's table of elliptic curves

510 = 2 · 3 · 5 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 17-	Signs for the Atkin-Lehner involutions
Class	510f	Isogeny class
Conductor	510	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1721250 = 2 · 34 · 54 · 17	Discriminant
Eigenvalues	2- 3- 5+  0  4  2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-186,-990]	[a1,a2,a3,a4,a6]
j	711882749089/1721250	j-invariant
L	2.5858436070631	L(r)(E,1)/r!
Ω	1.2929218035316	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	4080t4 16320r3 1530e4 2550a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 510f3

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

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Quadratic twists for elliptic curve 510f3

-4	8	-3	5	-7	-11	13	17
4080t4	16320r3	1530e4	2550a3	24990bp4	61710w4	86190bi4	8670r3

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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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