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	510d	Isogeny class
Conductor	510	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	478125000 = 23 · 32 · 58 · 17	Discriminant
Eigenvalues	2- 3+ 5+ -4 -4 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-6541,-206341]	[a1,a2,a3,a4,a6]
Generators	[-47:24:1]	Generators of the group modulo torsion
j	30949975477232209/478125000	j-invariant
L	2.1812264076948	L(r)(E,1)/r!
Ω	0.53087047736269	Real period
R	1.3695910777402	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	4080bb3 16320bn3 1530f3 2550k3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 510d3

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
-	+	+	-4	-4	-2	-	-4	-4	2	4	-6	2	-12	8	-2	12	2	4	-4	-14	-12	-4	10	18

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Quadratic twists for elliptic curve 510d3

-4	8	-3	5	-7	-11	13	17
4080bb3	16320bn3	1530f3	2550k3	24990cd4	61710c4	86190r4	8670bb3

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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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