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	48	Product of Tamagawa factors cp
Δ	-109596256200 = -1 · 23 · 38 · 52 · 174	Discriminant
Eigenvalues	2- 3+ 5+ -4 -4 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,579,-14757]	[a1,a2,a3,a4,a6]
Generators	[21:74:1]	Generators of the group modulo torsion
j	21464092074671/109596256200	j-invariant
L	2.1812264076948	L(r)(E,1)/r!
Ω	0.53087047736269	Real period
R	0.34239776943504	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	4080bb4 16320bn4 1530f4 2550k4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 510d4

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 510d4

-4	8	-3	5	-7	-11	13	17
4080bb4	16320bn4	1530f4	2550k4	24990cd3	61710c3	86190r3	8670bb4

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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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